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Publications HAL

2020

auteur
Diego Figueira, Santiago Figueira, Edwin Pin Baque
titre
Finite Controllability for Ontology-Mediated Query Answering of CRPQ  »
article
2020
resume
We study finite ontology mediated query answering (FOMQA), the variant of ontology mediated query answering (OMQA) where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. The query language we study is conjunctive two-way regular path queries (C2RPQ), which can be regarded as the result of adding simple recursion to Conjunctive Queries. We focus on understanding the finite-controllable fragments of C2RPQ, that is, on the question: for which fragments of C2RPQ the OMQA and FOMQA are equivalent? For graph classes S, we consider fragments C2RPQ(S) of C2RPQ as the queries whose underlying graph structure is in S. We completely classify the finite-controllable and non-finite-controllable fragments under: inclusion dependencies, (frontier-)guarded rules, frontier-one rules (either with or without constants), and more generally under guarded-negation first-order constraints. For the finite-controllable fragments, we show a reduction to the satisfiability problem for guarded-negation first-order logic, yielding a 2EXPTIME algorithm (in combined complexity) for the corresponding (F)OMQA problem.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-02508782/file/main-hal.pdfBibTex
auteur
Diego Figueira, Adwait Godbole, S. Krishna, Wim Martens, Matthias Niewerth, Tina Trautner
titre
Containment of Simple Regular Path Queries  »
article
2020
resume
Testing containment of queries is a fundamental reasoning task in knowledge representation. We study here the containment problem for Conjunctive Regular Path Queries (CRPQs), a navigational query language extensively used in ontology and graph database querying. While it is known that containment of CRPQs is expspace-complete in general, we focus here on severely restricted fragments, which are known to be highly relevant in practice according to several recent studies. We obtain a detailed overview of the complexity of the containment problem, depending on the features used in the regular expressions of the queries, with completeness results for np, pitwo, pspace or expspace.
Accès au bibtex
https://arxiv.org/pdf/2003.04411BibTex
auteur
Diego Figueira
titre
Containment of UC2RPQ: the hard and easy cases  »
article
International Conference on Database Theory (ICDT), Mar 2020, Copenhagen, Denmark. pp.9:1-9:18, ⟨10.4230/LIPIcs.ICDT.2020.9⟩
resume
We study the containment problem for UC2RPQ, that is, two-way Regular Path Queries, closed under conjunction, projection and union. We show a dichotomy property between PSpace-c and ExpSpace-c based on a property on the underlying graph of queries. We show that for any class C of graphs, the containment problem for queries whose underlying graph is in C is in PSpace if and only if C has bounded bridgewidth. Bridgewidth is a graph measure we introduce to this end, defined as the maximum size of a minimal edge separator of a graph.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-02291888/file/main.pdfBibTex
auteur
Wojciech Czerwiński, Diego Figueira, Piotr Hofman
titre
Universality Problem for Unambiguous VASS  »
article
2020
resume
We study languages of unambiguous VASS, that is, Vector Addition Systems with States, whose transitions read letters from a finite alphabet, and whose acceptance condition is defined by a set of final states (i.e., the coverability language). We show that the problem of universality for unambiguous VASS is ExpSpace-complete, in sheer contrast to Ackermann-completeness for arbitrary VASS, even in dimension 1. When the dimension d is fixed, the universality problem is PSpace-complete if d ≥ 2, and coNP-hard for 1-dimensional VASS (also known as One Counter Nets).
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-02483495/file/main.pdfBibTex

2019

auteur
Diego Figueira, Varun Ramanathan, Pascal Weil
titre
The Quantifier Alternation Hierarchy of Synchronous Relations  »
article
International Symposium on Mathematical Foundations of Computer Science (MFCS), Aug 2019, Aachen, Germany. pp.29:1-29:14, ⟨10.4230/LIPIcs.MFCS.2019.29⟩
resume
The class of synchronous relations, also known as automatic or regular, is one of the most studied subclasses of rational relations. It enjoys many desirable closure properties and is known to be logically characterized: the synchronous relations are exactly those that are defined by a first-order formula on the structure of all finite words, with the prefix, equal-length and last-letter predicates. Here, we study the quantifier alternation hierarchy of this logic. We show that it collapses at level \Sigma_3 and that all levels below admit decidable characterizations. Our results reveal the connections between this hierarchy and the well-known hierarchy of first-order defined languages of finite words.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-02109188/file/final-hal.pdfBibTex
auteur
Diego Figueira
titre
Co-finiteness of VASS coverability languages  »
article
2019
resume
We study the class of languages recognized by multi-counter finite state automata. These are finite automata reading letters from a finite alphabet A, equipped with n counters of natural numbers, which can be incremented or decremented by transitions. The acceptance condition requires the last state to be from the final set of states. This is equivalent to the language acceptors associated with coverability problems for labelled Petri Nets or labelled Vector Addition Systems with States (VASS). We show that the problem of whether the complement of the language has finitely many words (i.e., whether it is «almost equal» to A*) is decidable. We do this by a reduction to the universality problem (i.e., whether it is «equal» to A*).
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-02193089/file/main.pdfBibTex
auteur
Pablo Barceló, Diego Figueira, Miguel Romero
titre
Boundedness of Conjunctive Regular Path Queries  »
article
International Colloquium on Automata, Languages, and Programming (ICALP), Jul 2019, Patras, Greece. ⟨10.4230/LIPIcs.ICALP.2019.104⟩
resume
We study the boundedness problem for unions of conjunctive regular path queries with inverses (UC2RPQs). This is the problem of, given a UC2RPQ, checking whether it is equivalent to a union of conjunctive queries (UCQ). We show the problem to be ExpSpace-complete, thus coinciding with the complexity of containment for UC2RPQs. As a corollary, when a UC2RPQ is bounded, it is equivalent to a UCQ of at most triple-exponential size, and in fact we show that this bound is optimal. We also study better behaved classes of UC2RPQs, namely acyclic UC2RPQs of bounded thickness, and strongly connected UCRPQs, whose boundedness problem are, respectively, PSpace-complete and Pi^p_2-complete. Most upper bounds exploit results on limitedness for distance automata, in particular extending the model with alternation and two-wayness, which may be of independent interest.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-02056388/file/main-hal.pdfBibTex
auteur
María Emilia Descotte, Diego Figueira, Santiago Figueira
titre
Closure properties of synchronized relations  »
article
International Symposium on Theoretical Aspects of Computer Science (STACS), Mar 2019, Berlin, Germany. ⟨10.4230/LIPIcs.STACS.2019.22⟩
resume
A standard approach to define k-ary word relations over a finite alphabet A is through k-tape finite state automata that recognize regular languages L over {1,. .. , k} × A, where (i, a) is interpreted as reading letter a from tape i. Accordingly, a word w ∈ L denotes the tuple (u1,...,uk) ∈ (A*)^k in which ui is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of rational relations, enforcing restrictions on the reading regime from the tapes, which we call synchronization, yields various sub-classes of relations. Such synchronization restrictions are imposed through regular properties on the projection of the language L onto {1,..., k}. In this way, for each regular language C ⊆ {1,..., k}*, one obtains a class Rel(C) of relations. Synchronous, Recognizable, and Length-preserving rational relations are all examples of classes that can be defined in this way. We study basic properties of these classes of relations, in terms of closure under intersection, complement, concatenation, Kleene star and projection. We characterize the classes with each closure property. For the binary case (k = 2) this yields effective procedures.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01884574/file/main.pdfBibTex

2018

auteur
Diego Figueira
titre
On XPath with Reflexive-Transitive Axes and Data Tests  »
article
2018
resume
We study a logic on multi-attribute data trees. These are unranked ordered finite trees whose every node contains a label, and a vector of data values, one for each attribute. Labels belong to some finite alphabet, and data values to some infinite domain. Here, we show decidability of the satisfiability problem for XPath with data equality tests, where navigation can be done going downwards, rightwards or leftwards in the XML document. That is, where navigation is done using the reflexive-transitive XPath axes "descendant-or-self", "following-sibling-or-self", and "preceding-sibling-or-self".
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01832177/file/main.pdfBibTex
auteur
Diego Figueira, M. Praveen
titre
Playing with Repetitions in Data Words Using Energy Games  »
article
Annual Symposium on Logic in Computer Science (LICS), Jul 2018, Oxford, UK. ⟨10.1145/3209108.3209154⟩
resume
We introduce two-player games which build words over infinite alphabets, and we study the problem of checking the existence of winning strategies. These games are played by two players, who take turns in choosing valuations for variables ranging over an infinite data domain, thus generating multi-attributed data words. The winner of the game is specified by formulas in the Logic of Repeating Values, which can reason about repetitions of data values in infinite data words. We prove that it is undecidable to check if one of the players has a winning strategy, even in very restrictive settings. However, we prove that if one of the players is restricted to choose valuations ranging over the Boolean domain, the games are effectively equivalent to single-sided games on vector addition systems with states (in which one of the players can change control states but cannot change counter values), known to be decidable and effectively equivalent to energy games. Previous works have shown that the satisfiability problem for various variants of the logic of repeating values is equivalent to the reachability and coverability problems in vector addition systems. Our results raise this connection to the level of games, augmenting further the associations between logics on data words and counter systems.
Accès au bibtex
https://arxiv.org/pdf/1802.07435v2BibTex
auteur
María Emilia Descotte, Diego Figueira, Gabriele Puppis
titre
Resynchronizing Classes of Word Relations  »
article
International Colloquium on Automata, Languages, and Programming (ICALP), Jul 2018, Prague, Czech Republic. ⟨10.4230/LIPIcs.ICALP.2018.123⟩
resume
A natural approach to defining binary word relations over a finite alphabet A is through two-tape finite state automata, which can be seen as regular language L over {1,2}xA, where (i,a) is interpreted as reading letter a from tape i. Thus, a word w of the language L denotes the pair (u_1,u_2) \in A^* \times A^* in which u_i is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of Rational relations (a.k.a. non-deterministic finite state transducers), enforcing restrictions on the reading regime from the tapes, that we call synchronization, yields various sub-classes of relations. Such synchronization restrictions are imposed through regular properties on the projection of the language onto {1,2}. In this way, for each regular language C \subseteq {1,2}^*, one obtains a class Rel(C) of relations, such as the classes of Regular, Recognizable, or length-preserving relations, as well as (infinitely) many other classes. We study the problem of containment for synchronized classes of relations: given C,D \subseteq {1,2}^*, is Rel(C) \subseteq Rel(D)? We show a characterization in terms of C and D which gives a decidability procedure to test for class inclusion. This also yields a procedure to re-synchronize languages from {1,2}xA preserving the denoted relation whenever the inclusion holds.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01721046/file/main-hal.pdfBibTex
auteur
Sergio Abriola, Pablo Barceló, Diego Figueira, Santiago Figueira
titre
Bisimulations on Data Graphs  »
article
Journal of Artificial Intelligence Research, 2018, 61, pp.171-213. ⟨10.1613/jair.5637⟩
resume
Bisimulation provides structural conditions to characterize indistinguishability from an external observer between nodes on labeled graphs. It is a fundamental notion used in many areas, such as verification, graph-structured databases, and constraint satisfaction. However, several current applications use graphs where nodes also contain data (the so called " data graphs "), and where observers can test for equality or inequality of data values (e.g., asking the attribute 'name' of a node to be different from that of all its neighbors). The present work constitutes a first investigation of " data aware " bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath —a language that extends modal logics like PDL with tests for data equality— with and without transitive closure operators. We show that in general the problem is PSPACE-complete, but identify several restrictions that yield better complexity bounds (CO-NP, PTIME) by controlling suitable parameters of the problem, namely the amount of non-locality allowed, and the class of models considered (graphs, DAGs, trees). In particular, this analysis yields a hierarchy of tractable fragments.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01679889/file/version-homepage.pdfBibTex
auteur
Diego Figueira
titre
Satisfiability of XPath on data trees  »
article
ACM SIGLOG News, ACM, 2018, 5 (2), pp.4-16. ⟨10.1145/3212019.3212021⟩
resume
This is a survey on the satisfiability problem for XPath on data trees. Data trees are finite trees whose every node carries a label from a finite alphabet and a data value from an infinite domain. XPath is an expressive node selecting language for XML documents, which can be abstracted as data trees. Its satisfiability problem is in general undecidable. However, various fragments of XPath have decidable satisfiability problem, these are fragments defined in terms of the navigational axes which are allowed. We explore the state of the art in terms of decidability and discuss briefly some of the algorithmic techniques involved.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01670363/file/survey.pdfBibTex

2017

auteur
Diego Figueira, Ranko Lazić, Jérôme Leroux, Filip Mazowiecki, Grégoire Sutre
titre
Polynomial-Space Completeness of Reachability for Succinct Branching VASS in Dimension One  »
article
International Colloquium on Automata, Languages, and Programming (ICALP), Jul 2017, Warsaw, Poland. pp.119, ⟨10.4230/LIPIcs.ICALP.2017.119⟩
resume
Whether the reachability problem for branching vector addition systems, or equivalently the provability problem for multiplicative exponential linear logic, is decidable has been a long-standing open question. The one-dimensional case is a generalisation of the extensively studied one-counter nets, and it was recently established polynomial-time complete provided counter updates are given in unary. Our main contribution is to determine the complexity when the encoding is binary: polynomial-space complete.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01688742/file/main.pdfBibTex
auteur
Sergio Abriola, Diego Figueira, Santiago Figueira
titre
Logics of repeating values on data trees and branching counter systems  »
article
International Conference on Foundations of Software Science and Computation Structures (FoSSaCS), Apr 2017, Uppsala, Sweden
resume
We study connections between the satisfiability problem for logics on data trees and Branching Vector Addition Systems (BVAS). We consider a natural temporal logic of " repeating values " (LRV) featuring an operator which tests whether a data value in the current node is repeated in some descendant node. On the one hand, we show that the satisfiability of a restricted version of LRV on ranked data trees can be reduced to the coverability problem for Branching Vector Addition Systems. This immediately gives elementary upper bounds for its satisfiability problem, showing that restricted LRV behaves much better than downward-XPath, which has a non-primitive-recursive satisfiability problem. On the other hand, satisfiability for LRV is shown to be reducible to the coverability for a novel branching model we introduce here, called Merging VASS (MVASS). MVASS is an extension of Branching Vector Addition Systems with States (BVASS) allowing richer merging operations of the vectors. We show that the control-state reachability for MVASS, as well as its bottom-up coverability, are in 3ExpTime. This work can be seen as a natural continuation of the work initiated by Demri, D'Souza and Gascon for the case of data words, this time considering branching structures and counter systems, although, as we show, in the case of data trees more powerful models are needed to encode satisfiability.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01686713/file/main.pdfBibTex
auteur
Diego Figueira, Luc Segoufin
titre
Bottom-up automata on data trees and vertical XPath  »
article
Logical Methods in Computer Science, 2017, 13 (4), ⟨10.23638/LMCS-13(4:5)2017⟩
resume
A data tree is a finite tree whose every node carries a label from a finite alphabet and a datum from some infinite domain. We introduce a new model of automata over unranked data trees with a decidable emptiness problem. It is essentially a bottom-up alternating automaton with one register that can store one data value and can be used to perform equality tests with the data values occurring within the subtree of the current node. We show that it captures the expressive power of the vertical fragment of XPath —containing the child, descendant, parent and ancestor axes— obtaining thus a decision procedure for its satisfiability problem.
Accès au texte intégral et bibtex
https://hal.inria.fr/hal-01631219/file/1710.08748.pdfBibTex

2016

auteur
Diego Figueira, Piotr Hofman, Sławomir Lasota
titre
Relating timed and register automata  »
article
Mathematical Structures in Computer Science, Cambridge University Press, 2016, 26 (06), pp.993-1021. ⟨10.1017/S0960129514000322⟩
resume
Timed automata and register automata are well-known models of computation over timed and data words respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can store data values for later comparison. Although these two models behave in appearance differently, several decision problems have the same (un)decidability and complexity results for both models. As a prominent example, emptiness is decidable for alternating automata with one clock or register, both with non-primitive recursive complexity. This is not by chance. This work confirms that there is indeed a tight relationship between the two models. We show that a run of a timed automaton can be simulated by a register automaton over ordered data domain, and conversely that a run of a register automaton can be simulated by a timed automaton. These are exponential time reductions hold both in the finite and infinite words settings. Our results allow to transfer decidability results back and forth between these two kinds of models, as well complexity results modulo an exponential time reduction. We justify the usefulness of these reductions by obtaining new results on register automata.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01686366/file/main.pdfBibTex
auteur
Diego Figueira
titre
Semantically Acyclic Conjunctive Queries under Functional Dependencies  »
article
Annual Symposium on Logic in Computer Science (LICS), Jul 2016, New York, USA. ⟨10.1145/2933575.2933580⟩
resume
The evaluation problem for Conjunctive Queries (CQ) is known to be NP-complete in combined complexity and W[1]-hard in parameterized complexity. However, acyclic CQs and CQs of bounded tree-width can be evaluated in polynomial time in combined complexity and they are fixed-parameter tractable. We study the problem of whether a CQ can be rewritten into an equivalent CQ of bounded tree-width, in the presence of unary functional dependencies, assuming bounded arity signatures. We show that this problem is decidable in doubly exponential time, or in exponential time for a subclass of CQ's. When it exists, the algorithm also yields a witness query.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01713329/file/main.pdfBibTex
auteur
Myrto Arapinis, Diego Figueira, Marco Gaboardi
titre
Sensitivity of Counting Queries  »
article
International Colloquium on Automata, Languages, and Programming (ICALP), Jul 2016, Rome, Italy
resume
In the context of statistical databases, the release of accurate statistical information about the collected data often puts at risk the privacy of the individual contributors. The goal of differential privacy is to maximise the utility of a query while protecting the individual records in the database. A natural way to achieve differential privacy is to add statistical noise to the result of the query. In this context, a mechanism for releasing statistical information is thus a trade-off between utility and privacy. In order to balance these two "conflicting" requirements, privacy preserving mechanisms calibrate the added noise to the so-called sensitivity of the query, and thus a precise estimate of the sensitivity of the query is necessary to determine the amplitude of the noise to be added. In this paper, we initiate a systematic study of sensitivity of counting queries over relational databases. We first observe that the sensitivity of a Relational Algebra query with counting is not computable in general, and that while the sensitivity of Conjunctive Queries with counting is computable, it becomes unbounded as soon as the query includes a join. We then consider restricted classes of databases (databases with constraints), and study the problem of computing the sensitivity of a query given such constraints. We are able to establish bounds on the sensitivity of counting conjunctive queries over constrained databases. The kind of constraints studied here are: functional dependencies and cardinality dependencies. The latter is a natural generalisation of functional dependencies that allows us to provide tight bounds on the sensitivity of counting conjunctive queries
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01713317/file/icalp16.pdfBibTex
auteur
Sergio Abriola, Pablo Barceló, Diego Figueira, Santiago Figueira
titre
Bisimulations on Data Graphs  »
article
International Conference on Principles of Knowledge Representation and Reasoning (KR), Apr 2016, Cape Town, South Africa. pp.309-318
resume
Bisimulation provides structural conditions to characterize indistinguishability between nodes on graph-like structures from an external observer. It is a fundamental notion used in many areas. However, many applications use graphs where nodes have data, and where observers can test for equality or inequality of data values (e.g., asking the attribute 'name' of a node to be different from that of all its neighbors). The present work constitutes a first investigation of " data aware " bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational in-distinguishability for XPath —a language that extends modal logic with tests for data equality. We show that in general the problem is PSPACE-complete, but identify several restrictions that yield better complexity bounds (CO-NP, PTIME) by controlling suitable parameters of the problem; namely, the amount of non-locality allowed, and the class of models considered (graph, DAG, tree). In particular, this analysis yields a hierarchy of tractable fragments.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01713325/file/main.pdfBibTex
auteur
Stéphane Demri, Diego Figueira, M. Praveen
titre
Reasoning about Data Repetitions with Counter Systems  »
article
Logical Methods in Computer Science, 2016, 12 (3), ⟨10.2168/LMCS-12(3:1)2016⟩
resume
We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or past. We demonstrate correspondences between satisfiability problems for logics and reachability-like decision problems for counter systems. We show that allowing/disallowing atomic formulas expressing repetitions of values in the past corresponds to the reachability/coverability problem in Petri nets. This gives us 2expspace upper bounds for several satisfiability problems. We prove matching lower bounds by reduction from a reachability problem for a newly introduced class of counter systems. This new class is a succinct version of vector addition systems with states in which counters are accessed via pointers, a potentially useful feature in other contexts. We strengthen further the correspondences between data logics and counter systems by characterizing the complexity of fragments, extensions and variants of the logic. For instance, we precisely characterize the relationship between the number of attributes allowed in the logic and the number of counters needed in the counter system.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01685180/file/main.pdfBibTex

2015

auteur
Diego Figueira, Leonid Libkin
titre
Synchronizing Relations on Words  »
article
Theory of Computing Systems, Springer, 2015, 57 (2), pp.287 - 318. ⟨10.1007/s00224-014-9584-2⟩
resume
While the theory of languages of words is very mature, our understanding of relations on words is still lagging behind. And yet such relations appear in many new applications such as verification of pa-rameterized systems, querying graph-structured data, and information extraction, for instance. Classes of well-behaved relations typically used in such applications are obtained by adapting some of the equivalent definitions of regularity of words for relations, leading to non-equivalent notions of recognizable, regular, and rational relations. The goal of this paper is to propose a systematic way of defining classes of relations on words, of which these three classes are just natural examples, and to demonstrate its advantages compared to some of the standard techniques for studying word relations. The key idea is that of a synchronization of a pair of words, which is a word over an extended alphabet. Using it, we define classes of relations via classes of regular languages over a fixed alphabet, just {1, 2} for binary relations. We characterize some of the standard classes of relations on words via finiteness of parameters of synchronization languages, called shift, lag, and shiftlag. We describe these conditions in terms of the structure of cycles of graphs underlying automata, thereby showing their decidability. We show that for these classes there exist canonical synchronization languages, and every class of relations can be effectively re-synchronized using those canonical representatives. We also give sufficient conditions on synchronization languages, defined in terms of injectivity and surjectivity of their Parikh images, that guarantee closure under intersection and complement of the classes of relations they define.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01778459/file/hal.pdfBibTex
auteur
Diego Figueira, Leonid Libkin
titre
Path Logics for Querying Graphs: Combining Expressiveness and Efficiency  »
article
Annual Symposium on Logic in Computer Science (LICS), Jul 2015, Kyoto, Japan. ⟨10.1109/LICS.2015.39⟩
resume
We study logics expressing properties of paths in graphs that are tailored to querying graph databases: a data model for new applications such as social networks, the Semantic Web, biological data, crime detection, and others. The basic construct of such logics, a regular path query, checks for paths whose labels belong to a regular language. These logics fail to capture two commonly needed features: counting properties, and the ability to compare paths. It is known that regular path-comparison relations (e.g., prefix or equality) can be added without significant complexity overhead; however, adding common relations often demanded by applications (e.g., subword, subsequence, suffix) results in either undecidability or astronomical complexity. We propose, as a way around this problem, to use automata with counting functionalities, namely Parikh automata. They express many counting properties directly, and they approximate many relations of interest. We prove that with Parikh automata defining both languages and relations used in queries, we retain the low complexity of the standard path logics for graphs. In particular, this gives us efficient approximations to queries with prohibitively high complexity. We extend the best known decidability results by showing that even more expressive classes of relations are possible in query languages (sometimes with restriction on the shape of formulae). We also show that Parikh automata admit two convenient representations by analogs of regular expressions, making them usable in real-life querying.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01778476/file/epl.pdfBibTex
auteur
Diego Figueira, Santiago Figueira, Carlos Areces
titre
Model Theory of XPath on Data Trees. Part I: Bisimulation and Characterization  »
article
Journal of Artificial Intelligence Research, 2015
resume
We investigate model theoretic properties of XPath with data (in)equality tests over the class of data trees, i.e., the class of trees where each node contains a label from a finite alphabet and a data value from an infinite domain. We provide notions of (bi)simulations for XPath logics containing the child, parent, ancestor and descendant axes to navigate the tree. We show that these notions precisely characterize the equivalence relation associated with each logic. We study formula complexity measures consisting of the number of nested axes and nested subformulas in a formula; these notions are akin to the notion of quantifier rank in first-order logic. We show characterization results for fine grained notions of equivalence and (bi)simulation that take into account these complexity measures. We also prove that positive fragments of these logics correspond to the formulas preserved under (non-symmetric) simulations. We show that the logic including the child axis is equivalent to the fragment of first-order logic invariant under the corresponding notion of bisimulation. If upward navigation is allowed the characterization fails but a weaker result can still be established. These results hold both over the class of possibly infinite data trees and over the class of finite data trees. Besides their intrinsic theoretical value, we argue that bisimulations are useful tools to prove (non)expressivity results for the logics studied here, and we substantiate this claim with examples.
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01778416/file/main-hal.pdfBibTex

2014

auteur
Diego Figueira, Leonid Libkin
titre
Pattern logics and auxiliary relations  »
article
CSL-LICS'14, joint EACSL Annual Conference on Computer Science Logic (CSL) and Annual Symposium on Logic in Computer Science (LICS), Jul 2014, Vienna, Austria. ⟨10.1145/2603088.2603136⟩
resume
A common theme in the study of logics over finite structures is adding auxiliary predicates to enhance expressiveness and convey additional information. Examples include adding an order or arithmetic for capturing complexity classes, or the power of real-life declarative languages. A recent trend is to add a data-value comparison relation to words, trees, and graphs, for capturing modern data models such as XML and graph databases. Such additions often result in the loss of good properties of the underlying logic. Our goal is to show that such a loss can be avoided if we use pattern-based logics, standard in XML and graph data querying. The essence of such logics is that auxiliary relations are tested locally with respect to other relations in the structure. These logics are shown to admit strong versions of Hanf and Gaifman locality theorems, which are used to prove a homomorphism preservation theorem, and a decidability result for the satisfiability problem. We discuss applications of these results to pattern logics over data forests, and consequently to querying XML data.
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https://hal.archives-ouvertes.fr/hal-01793593/file/hal.pdfBibTex
auteur
Diego Figueira, Leonid Libkin
titre
Synchronizing Relations on Words  »
article
International Symposium on Theoretical Aspects of Computer Science (STACS), May 2014, Lyon, France
resume
While the theory of languages of words is very mature, our understanding of relations on words is still lagging behind. And yet such relations appear in many new applications such as verification of parameterized systems, querying graph-structured data, and information extraction, for instance. Classes of well-behaved relations typically used in such applications are obtained by adapting some of the equivalent definitions of regularity of words for relations, leading to non-equivalent notions of recognizable, regular, and rational relations. The goal of this paper is to propose a systematic way of defining classes of relations on words, of which these three classes are just natural examples, and to demonstrate its advantages compared to some of the standard techniques for studying word relations. The key idea is that of a synchronization of a pair of words, which is a word over an extended alphabet. Using it, we define classes of relations via classes of regular languages over a fixed alphabet, just {1, 2} for binary relations. We characterize some of the standard classes of relations on words via finiteness of parameters of synchronization languages, called shift, lag, and shiftlag. We describe these conditions in terms of the structure of cycles of graphs underlying automata, thereby showing their decidability. We show that for these classes there exist canonical synchronization languages, and every class of relations can be effectively re-synchronized using those canonical representatives. We also give sufficient conditions on synchronization languages, defined in terms of injectivity and surjectivity of their Parikh images, that guarantee closure under intersection and complement of the classes of relations they define.
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https://hal.archives-ouvertes.fr/hal-01793633/file/hal.pdfBibTex
auteur
Diego Figueira, Santiago Figueira, Carlos Areces
titre
Basic Model Theory of XPath on Data Trees  »
article
International Conference on Database Theory (ICDT), Mar 2014, Athens, Greece
resume
We investigate model theoretic properties of XPath with data (in)equality tests over the class of data trees, i.e., the class of trees where each node contains a label from a finite alphabet and a data value from an infinite domain. We provide notions of (bi)simulations for XPath logics containing the child, descendant, parent and ancestor axes to navigate the tree. We show that these notions precisely characterize the equivalence relation associated with each logic. We study formula complexity measures consisting of the number of nested axes and nested subformulas in a formula; these notions are akin to the notion of quantifier rank in first-order logic. We show characterization results for fine grained notions of equivalence and (bi)simulation that take into account these complexity measures. We also prove that positive fragments of these logics correspond to the formulas preserved under (non-symmetric) simulations. We show that the logic including the child axis is equivalent to the fragment of first-order logic invariant under the corresponding notion of bisimulation. If upward navigation is allowed the characterization fails but a weaker result can still be established. These results hold over the class of possibly infinite data trees and over the class of finite data trees. Besides their intrinsic theoretical value, we argue that bi-simulations are useful tools to prove (non)expressivity results for the logics studied here, and we substantiate this claim with examples.
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https://hal.archives-ouvertes.fr/hal-01793608/file/hal.pdfBibTex

2013

auteur
Stéphane Demri, Diego Figueira, M. Praveen
titre
Reasoning about Data Repetitions with Counter Systems  »
article
Annual/ACM Symposium on Logic in Computer Science (LICS), Jun 2013, New Orleans (LA), USA. ⟨10.1109/LICS.2013.8⟩
resume
We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or past. We demonstrate correspondences between satisfiability problems for logics and reachability-like decision problems for counter systems. We show that allowing/disallowing atomic formulas expressing repetitions of values in the past corresponds to the reachability/coverability problem in Petri nets. This gives us 2EXPSPACE upper bounds for several satisfiability problems. We prove matching lower bounds by reduction from a reachability problem for a newly introduced class of counter systems. This new class is a succinct version of vector addition systems with states in which counters are accessed via pointers, a potentially useful feature in other contexts. We strengthen further the correspondences between data logics and counter systems by characterizing the complexity of fragments, extensions and variants of the logic. For instance, we precisely characterize the relationship between the number of attributes allowed in the logic and the number of counters needed in the counter system.
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https://hal.archives-ouvertes.fr/hal-01795130/file/_lics13-with-appendix.pdfBibTex
auteur
Diego Figueira
titre
On XPath with transitive axes and data tests  »
article
Symposium on Principles of Database Systems (PODS), Jun 2013, New York (NY), USA. ⟨10.1145/2463664.2463675⟩
resume
We study the satisfiability problem for XPath with data equality tests. XPath is a node selecting language for XML documents whose satisfiability problem is known to be unde-cidable, even for very simple fragments. However, we show that the satisfiability for XPath with the rightward, leftward and downward reflexive-transitive axes (namely following-sibling-or-self, preceding-sibling-or-self, descendant-or-self) is decidable. Our algorithm yields a complexity of 3ExpSpace, and we also identify an expressive-equivalent normal form for the logic for which the satisfiability problem is in 2Exp-Space. These results are in contrast with the undecidabil-ity of the satisfiability problem as soon as we replace the reflexive-transitive axes with just transitive (non-reflexive) ones.
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https://hal.archives-ouvertes.fr/hal-01795148/file/hal.pdfBibTex
auteur
Pablo Barceló, Diego Figueira, Leonid Libkin
titre
Graph Logics with Rational Relations  »
article
Logical Methods in Computer Science, 2013, 9 (3), ⟨10.2168/LMCS-9(3:1)2013⟩
resume
We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword or subsequence. Evaluating formulae in such extended graph logics boils down to checking nonemptiness of the intersection of rational relations with regular or recognizable relations (or, more generally, to the generalized intersection problem, asking whether some projections of a regular relation have a nonempty intersection with a given rational relation). We prove that for several basic and commonly used rational relations, the intersection problem with regular relations is either undecidable (e.g., for subword or suffix, and some generalizations), or decidable with non-primitive-recursive complexity (e.g., for sub-sequence and its generalizations). These results are used to rule out many classes of graph logics that freely combine regular and rational relations, as well as to provide the simplest problem related to verifying lossy channel systems that has non-primitive-recursive complexity. We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classifies them into either efficiently checkable or undecidable cases. We also give examples of rational relations for which such logics are decidable even without syntactic restrictions.
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https://hal.archives-ouvertes.fr/hal-01795115/file/lrr.pdfBibTex
auteur
Diego Figueira
titre
Satisfiability for two-variable logic with two successor relations on finite linear orders  »
article
2013
resume
We study the finitary satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders. We show that the problem is decidable in NEXPTIME.
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https://arxiv.org/pdf/1204.2495BibTex

2012

auteur
Diego Figueira
titre
Decidability of Downward XPath  »
article
ACM Transactions on Computational Logic, ACM, 2012, 13 (4), pp.1-40. ⟨10.1145/2362355.2362362⟩
resume
We investigate the satisfiability problem for downward-XPath, the fragment of XPath that includes the child and descendant axes, and tests for (in)equality of attributes' values. We prove that this problem is decidable, ExpTime-complete. These bounds also hold when path expressions allow closure under the Kleene star operator. To obtain these results, we introduce a Downward Data automata model (DD automata) over trees with data, which has a decidable emptiness problem. Satisfiability of downward-XPath can be reduced to the emptiness problem of DD automata and hence its decidability follows. Although downward-XPath does not include any horizontal axis, DD automata are more expressive and can perform some horizontal tests. Thus, we show that the satisfiability remains in ExpTime even in the presence of the regular constraints expressible by DD automata. However, the same problem in the presence of any regular constraint is known to have a non-primitive recursive complexity. Finally, we give the exact complexity of the satisfiability problem for several fragments of downward-XPath.
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https://hal.archives-ouvertes.fr/hal-01799714/file/main-with-app.pdfBibTex
auteur
Pablo Barceló, Diego Figueira, Leonid Libkin
titre
Graph Logics with Rational Relations and the Generalized Intersection Problem  »
article
Annual Symposium on Logic in Computer Science (LICS), Jun 2012, Dubrovnik, Croatia. pp.115-124, ⟨10.1109/LICS.2012.23⟩
resume
We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword (factor) or subsequence. Evaluating formulae in such extended graph logics boils down to checking non-emptiness of the intersection of rational relations with regular or recognizable relations (or, more generally, to the generalized intersection problem, asking whether some projections of a regular relation have a nonempty intersection with a given rational relation). We prove that for several basic and commonly used rational relations, the intersection problem with regular relations is either undecidable (e.g., for subword or suffix, and some generalizations), or decidable with non-multiply-recursive complexity (e.g., for subsequence and its generalizations). These results are used to rule out many classes of graph logics that freely combine regular and rational relations, as well as to provide the simplest problem related to verifying lossy channel systems that has non-multiply-recursive complexity. We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classifies them into either efficiently checkable or undecidable cases. We also give examples of rational relations for which such logics are decidable even without syntactic restrictions.
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https://hal.archives-ouvertes.fr/hal-01799740/file/lics12.pdfBibTex
auteur
Vince Bárány, Mikołaj Bojańczyk, Diego Figueira, Paweł Parys
titre
Decidable classes of documents for XPath  »
article
Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 2012, Hyderabad, India. pp.99-111
resume
We study the satisfiability problem for XPath over XML documents of bounded depth. We define two parameters, called match width and braid width, that assign a number to any class of documents. We show that for all k, satisfiability for XPath restricted to bounded depth documents with match width at most k is decidable; and that XPath is undecidable on any class of documents with unbounded braid width. We conjecture that these two parameters are equivalent, in the sense that a class of documents has bounded match width iff it has bounded braid width.
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https://hal.archives-ouvertes.fr/hal-01799733/file/dataminor-app.pdfBibTex
auteur
Diego Figueira
titre
Alternating register automata on finite words and trees  »
article
Logical Methods in Computer Science, 2012, 8 (1), pp.1-44. ⟨10.2168/LMCS-8(1:22)2012⟩
resume
We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate one-way automata with alternating control over data words or trees, with one register for storing data and comparing them for equality. This is a continuation of the study started by Demri, Lazic and Jurdzinski. From the standpoint of register automata models, this work aims at two objectives: (1) simplifying the existent decidability proofs for the emptiness problem for alternating register automata; and (2) exhibiting decidable extensions for these models. From the logical perspective, we show that (a) in the case of data words, satisfiability of LTL with one register and quantification over data values is decidable; and (b) the satisfiability problem for the so-called forward fragment of XPath on xml documents is decidable, even in the presence of DTDs and even of key constraints. The decidability is obtained through a reduction to the automata model introduced. This fragment contains the child, descendant, next-sibling and following-sibling axes, as well as data equality and inequality tests.
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https://hal.archives-ouvertes.fr/hal-01799710/file/main2.pdfBibTex

2011

auteur
Diego Figueira
titre
A Decidable Two-Way Logic on Data Words  »
article
Annual Symposium on Logic in Computer Science (LICS), Jun 2011, Toronto, Canada. ⟨10.1109/LICS.2011.18⟩
resume
We study the satisfiability problem for a logic on data words. A data word is a finite word where every position carries a label from a finite alphabet and a data value from an infinite domain. The logic we consider is two-way, contains " future " and " past " modalities, where these are considered as reflexive and transitive relations, and data equality and inequality tests. This logic corresponds to the fragment of XPath with the 'following-sibling-or-self' and 'preceding-sibling-or-self' axes over a data word. We show that this problem is decidable, EXPSPACE-complete. This is surprising considering that with the strict navigation relations (non-reflexive) the satisfiability problem is undecidable. To show this we first reduce the problem to a derivation problem for an infinite transition system, and then we show how to abstract this problem into a reachability problem of a finite transition system.
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https://hal.archives-ouvertes.fr/hal-01803452/file/reftran.pdfBibTex
auteur
Mikołaj Bojańczyk, Diego Figueira
titre
Efficient evaluation for a temporal logic on changing XML documents  »
article
Symposium on Principles of Database Systems (PODS), Jun 2011, Athens, Greece. ⟨10.1145/1989284.1989317⟩
resume
We consider a sequence t1,. .. , tk of XML documents that is produced by a sequence of local edit operations. To describe properties of such a sequence, we use a temporal logic. The logic can navigate both in time and in the document, e.g. a formula can say that every node with label a eventually gets a descendant with label b. For every fixed formula, we provide an evaluation algorithm that works in time O(k·log(n)), where k is the number of edit operations and n is the maximal size of document that is produced. In the algorithm, we represent formulas of the logic by a kind of automaton, which works on sequences of documents. The algorithm works on XML documents of bounded depth.
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https://hal.archives-ouvertes.fr/hal-01803459/file/hal.pdfBibTex
auteur
Diego Figueira, Santiago Figueira, Sylvain Schmitz, Philippe Schnoebelen
titre
Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma  »
article
Annual Symposium on Logic in Computer Science (LICS), Jun 2011, Toronto, Canada. p. 269-278, ⟨10.1109/LICS.2011.39⟩
resume
Dickson's Lemma is a simple yet powerful tool widely used in termination proofs, especially when dealing with counters or related data structures. However, most computer scientists do not know how to derive complexity upper bounds from such termination proofs, and the existing literature is not very helpful in these matters. We propose a new analysis of the length of bad sequences over (N^k,\leq) and explain how one may derive complexity upper bounds from termination proofs. Our upper bounds improve earlier results and are essentially tight.
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https://arxiv.org/pdf/1007.2989BibTex
auteur
Carlos Areces, Diego Figueira, Santiago Figueira, Sergio Mera
titre
The expressive power of Memory Logics  »
article
The Review of Symbolic Logic, Cambridge University Press, 2011, 4 (2), pp.290-318. ⟨10.1017/S1755020310000389⟩
resume
We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic HL(↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain. This work focuses in the case where the memory is a set, and we can test whether the current node belongs to the set or not. We prove that, in terms of expressive power, the memory logics we discuss here lie between the basic modal logic K and HL(↓). We show that the satisfiability problem of most of the logics we cover is undecidable. The only logic with a decidable satisfiability problem is obtained by imposing strong constraints on which elements can be memorized.
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https://hal.archives-ouvertes.fr/hal-01803447/file/epm.pdfBibTex
auteur
Diego Figueira, Luc Segoufin
titre
Bottom-up automata on data trees and vertical XPath  »
article
Symposium on Theoretical Aspects of Computer Science (STACS), Mar 2011, Dortmund, Germany. pp.93-104
resume
A data tree is a tree whose every node carries a label from a finite alphabet and a datum from some infinite domain. We introduce a new model of automata over unranked data trees with a decidable emptiness problem. It is essentially a bottom-up alternating automaton with one register, enriched with epsilon-transitions that perform tests on the data values of the subtree. We show that it captures the expressive power of the vertical fragment of XPath —containing the child, descendant, parent and ancestor axes— obtaining thus a decision procedure for its satisfiability problem.
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https://hal.archives-ouvertes.fr/hal-00573596/file/12.pdfBibTex

2010

auteur
Diego Figueira
titre
Reasoning on words and trees with data  »
article
École normale supérieure de Cachan - ENS Cachan (now ENS Paris-Saclay), 2010. ⟨NNT : 2010DENS0041⟩
resume
A data word (resp. a data tree) is a finite word (resp. tree) whose every position carries a letter from a finite alphabet and a datum form an infinite domain. In this thesis we investigate automata and logics for data words and data trees with decidable reasoning problems: we focus on the emptiness problem in the case of automata, and the satisfiability problem in the case of logics. On data words, we present a decidable extension of the model of alternating register automata studied by Demri and Lazic. Further, we show the decidability of the satisfiability problem for the linear-time temporal logic on data words LTL↓(X, F, U) (studied by Demri and Lazic) with quantifi-cation over data values. We also prove that the lower bounds of non-primitive recursiveness shown by Demri and Lazic for LTL↓(X, F) carry over to LTL↓(F). On data trees, we consider three decidable automata models with diff-erent characteristics. We first introduce the Downward Data automaton (DD automata). Its execution consists in a transduction of the finite labeling of the tree, and a verifi-cation of data properties for every subtree of the transduced tree. This model is closed under boolean operations, but the tests it can make on the order of the siblings is very limited. Its emptiness problem is 2ExpTime. On the contrary, the other two automata models we introduce have an emptiness problem with a non-primitive recursive complexity, and are closed under intersection and union, but not complementation. They are both alternating automata with one register to store and compare data values. The automata class ATRA(guess, spread) extends the top-down automata ATRA of Jurdzinski and Lazic. We exhibit similar decidable extensions as the one showed in the case of data words. This class can test for any tree regular language—in contrast to DD automata. Finally, we consider a bottom-up alternating tree automaton with one register (called BUDA). Although the BUDA class is one-way, it has features that allow to test data properties by navigating the tree in both directions: upward and downward. In opposition to ATRA(guess, spread), this automaton cannot test for properties on the the sequence of siblings (like, for example, the order in which labels appear). All these three models have connections with the logic XPath—a logic conceived for xml documents, which can be seen as data trees. Through the aforementioned automata we show that the satisfiability of three natural fragments of XPath are decidable. These fragments are: downward XPath, where navigation can only be done by child and descendant axes; forward XPath, where navigation also contains the next sibling axis and its transitive closure; and vertical XPath, whose navigation consists in the child, descendant, parent and ancestor axes. Whereas downward XPath is ExpTime-complete, forward and vertical XPath have non-primitive recursive lower bounds.
Accès au texte intégral et bibtex
https://tel.archives-ouvertes.fr/tel-00718605/file/Figueira2010.pdfBibTex
auteur
Diego Figueira, Piotr Hofman, Sławomir Lasota
titre
Relating timed and register automata  »
article
International Workshop on Expressiveness in Concurrency (EXPRESS), Aug 2010, Paris, France. pp.61-75, ⟨10.4204/EPTCS.41.5⟩
resume
Timed automata and register automata are well-known models of computation over timed and data words respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can store data values for later comparison. Although these two models behave in appearance differently, several decision problems have the same (un)decidability and complexity results for both models. As a prominent example, emptiness is decidable for alternating automata with one clock or register, both with non-primitive recursive complexity. This is not by chance. This work confirms that there is indeed a tight relationship between the two models. We show that a run of a timed automaton can be simulated by a register automaton, and conversely that a run of a register automaton can be simulated by a timed automaton. Our results allow to transfer complexity and decidability results back and forth between these two kinds of models. We justify the usefulness of these reductions by obtaining new results on register automata.
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https://hal.archives-ouvertes.fr/hal-01806104/file/timedata.pdfBibTex
auteur
Diego Figueira
titre
Forward-XPath and extended register automata  »
article
International Conference on Database Theory (ICDT), Mar 2010, Lausanne, Switzerland. ⟨10.1145/1804669.1804699⟩
resume
We consider a fragment of XPath named 'forward-XPath', which contains all descendant and rightwards sibling axes as well as data equality and inequality tests. The satisfiability problem for forward-XPath in the presence of DTDs and even of primary key constraints is shown here to be decidable. To show decidability we introduce a model of alternating au-tomata on data trees that can move downwards and right-wards in the tree, have one register for storing data and compare them for equality, and have the ability to (1) non-deterministically guess a data value and store it, and (2) quantify universally over the set of data values seen so far during the run. This model extends the work of Jurdzinski and Lazic. Decidability of the finitary non-emptiness problem for this model is obtained by a direct reduction to a well-structured transition system, contrary to previous approaches. Another consequence that we explore is the satis-fiability problem for the Linear Temporal Logic (LTL) over data words with one register and quantification over data values, which is shown to be decidable.
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https://hal.archives-ouvertes.fr/hal-01806093/file/mainhal.pdfBibTex

2009

auteur
Diego Figueira, Luc Segoufin
titre
Future-looking Logics on Data Words and Trees  »
article
International Symposium on Mathematical Foundations of Computer Science (MFCS), Aug 2009, Novy Smokovec, Slovakia. pp.331-343
resume
In a data word or a data tree each position carries a label from a finite alphabet and a data value from an infinite domain. Over data words we consider the logic LTL_↓^1 (F), that extends LTL(F) with one register for storing data values for later comparisons. We show that satisfiability over data words of LTL_↓^1 (F) is already non primitive recursive. We also show that the extension of LTL_↓^1 (F) with either the backward modality F^{−1} or with one extra register is undecidable. All these lower bounds were already known for LTL_↓^1(X, F) and our results essentially show that the X modality was not necessary. Moreover we show that over data trees similar lower bounds hold for certain fragments of XPath.
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https://hal.archives-ouvertes.fr/hal-01806188/file/transitive-words.pdfBibTex
auteur
Carlos Areces, Diego Figueira
titre
Which Semantics for Neighbourhood Semantics?  »
article
International Joint Conference on Artificial Intelligence (IJCAI), Jul 2009, Pasadena (CA), USA. pp.671-676
resume
In this article we discuss two alternative proposals for neighbourhood semantics (which we call strict and loose neighbourhood semantics, Ny =intarondduNce respectively) that have been previously introduced in the literature. Our main tools are suitable notions of bisimulation. While an elegant notion of bisimulation exists for N, the required bisimulation for N= is rather involved. We propose a simple extension of N= with a universal modality that we call N=(E), which comes together with a natural notion of bisimulation. We also investigate the complexity of the satisfiability problem for N and N=(E).
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auteur
Carlos Areces, Diego Figueira, Daniel Gorin, Sergio Mera
titre
Tableaux and Model Checking for Memory Logics  »
article
International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX), Jul 2009, Oslo, Norway. pp.47-61
resume
Memory logics are modal logics whose semantics is specified in terms of relational models enriched with additional data structure to represent memory. The logical language is then extended with a collection of operations to access and modify the data structure. In this paper we study their satisfiability and the model checking problems. We first give sound and complete tableaux calculi for the memory logic ML(k ; r ; e ) (the basic modal language extended with the operator r used to memorize a state, the operator e used to wipe out the memory, and the operator k used to check if the current point of evaluation is memorized) and some of its sublanguages. As the satisfiability problem of ML( k ; r ; e ) is undecidable, the tableau calculus we present is non terminating. Hence, we furthermore study a variation that ensures termination, at the expense of completeness, and we use model checking to ensure soundness. Secondly, we show that the model checking problem is PSpace-complete.
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BibTex
auteur
Diego Figueira
titre
Satisfiability of Downward XPath with Data Equality Tests  »
article
Symposium on Principles of Database Systems (PODS), Jun 2009, Providence (RI), USA
resume
In this work we investigate the satisfiability problem for the logic XPath(↓*, ↓, =), that includes all downward axes as well as equality and inequality tests. We address this problem in the absence of DTDs and the sibling axis. We prove that this fragment is decidable, and we nail down its complexity, showing the problem to be ExpTime-complete. The result also holds when path expressions allow closure under the Kleene star operator. To obtain these results, we introduce a new automaton model over data trees that captures XPath(↓*, ↓, =) and has an ExpTime emptiness problem. Furthermore, we give the exact complexity of several downward-looking fragments.
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https://hal.archives-ouvertes.fr/hal-02382925/file/xpdown-hal.pdfBibTex

2008

auteur
Carlos Areces, Diego Figueira, Santiago Figueira, Sergio Mera
titre
Expressive Power and Decidability for Memory Logics  »
article
Workshop on Logic, Language, Information and Computation (WoLLIC), Jul 2008, Edinburgh, UK
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