The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
An automata-theoretic approach to linear temporal logic
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Handbook of formal languages, vol. 1
Varieties Of Formal Languages
Cascade Decompositions are Bit-Vector Algorithms
CIAA '01 Revised Papers from the 6th International Conference on Implementation and Application of Automata
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Classifying discrete temporal properties
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
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Determining for a given deterministic complete automaton the sequence of visited states while reading a given word is the core of important problems with automata-based solutions, such as approximate string matching. The main difficulty is to do this computation efficiently. Considering words as vectors and working on them using vectorial operations allows to solve the problem faster than using local operations.In this paper, we show first that the set of vectorial operations needed by an algorithm representing a given automaton depends on the language accepted by the automaton. We give precise characterizations for star-free, solvable and regular languages using vectorial algorithms. We also study classes of languages associated with restricted sets of vectorial operations and relate them with languages defined by fragments of linear temporal logic.Finally, we consider the converse problem of constructing an automaton from a given vectorial algorithm. As a byproduct, we show that the satisfiability problem for some extensions of LTL characterizing solvable and regular languages is PSPACE-complete.