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X-WR-CALNAME:[LX] Andrew Ryzhikov -- From unambiguous finite automata to fi
 nite semigroups of rational matrices
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TZUNTIL:20271031T010000Z
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DESCRIPTION:A nondeterministic finite automaton (without initial and final 
 states) is called unambiguous (or diamond-free) if for every two states p\
 , q and every word w there is at most one path from p to q labelled by w. 
 Such automata naturally appear in the context of variable-length codes\, u
 nambiguous monoids of relations and weighted automata. An NFA (again\, wit
 hout initial and final states) is called complete if every word labels som
 e path in it. I will discuss how to decide if an unambiguous finite automa
 ton is complete and how to estimate the length of a shortest word violatin
 g completeness.\nI will then move to the setting of matrix semigroups\, in
  which unambiguous automata are nothing more than semigroups of matrices w
 hose entries are only zero and one\, and incompleteness is just matrix mor
 tality ('does the zero matrix belong to a matrix semigroup?'). This (predi
 ctable) plot twist will allow me to generalise the setting of unambiguous 
 automata to the case of finite semigroups of matrices with rational entrie
 s\, and to state some bold conjectures.\n\n\nImport automatique depuis htt
 ps://framagenda.org/remote.php/dav/public-calendars/D3yqF7nwys9amfyY?expor
 t par sync_icals_to_drupal.py pour M2F
DTSTART;TZID=Europe/Paris:20251007T140000
DTEND;TZID=Europe/Paris:20251007T150000
LOCATION:sale 178
SEQUENCE:0
SUMMARY:[LX] Andrew Ryzhikov -- From unambiguous finite automata to finite 
 semigroups of rational matrices
TRANSP:OPAQUE
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