On continuous timed automata with input-determined guards,
Fabrice Chevalier (LSV), Deepak D'Souza (CSA, IISc), Pavithra Prabhakar (CSA, IISc).
We consider a general class of timed automata parameterized by a set of
“input-determined” operators, in a continuous time setting.
We show that for any such set of operators, we have a monadic second
order logic characterization of the class of timed languages accepted
by the corresponding class of automata. Further, we consider natural
timed temporal logics based on these operators, and show that they are
expressively equivalent to the first-order fragment of the
corresponding MSO logics. As a corollary of these general results we
obtain an expressive completeness result for the continuous version of
FSTTCS'06, Lect. Notes in Computer Science, Springer 2006