Complexity of automata.- Compressed automata.- Counter automata.- Dictionary matching.- Edit distance.- Homing sequences.- Implementation.- Minimization of automata.- Model checking.- Parsing of regular expressions.- Partial word automata.- Picture languages.- Pushdown automata.- Queue automata.- Reachability analysis for software verification.- Restarting automata.- Transducers.- Tree automata.- Weighted automata.- XML streams.

We extend the weak monadic second-order logic of one successor on finite strings (M2L-STR) to symbolic alphabets by allowing character predicates to range over decidable quantifier free theories instead of finite alphabets. We call this logic, which is able to describe sequences over complex and potentially infinite domains, symbolic M2L-STR (S-M2L-STR). We then present a decision procedure for S-M2L-STR based on a reduction to symbolic finite automata, a decidable extension of finite automata that allows transitions to carry predicates and can therefore model symbolic alphabets. The reduction constructs a symbolic automaton over an alphabet consisting of pairs of symbols where the first element of the pair is a symbol in the original formula’s alphabet, while the second element is a bit-vector. To handle this modified alphabet we show that the Cartesian product of two decidable Boolean algebras (e.g., the formula’s one and the bit-vector’s one) also forms a decidable Boolean algebras. To make the decision procedure practical, we propose two efficient representations of the Cartesian product of two Boolean algebras, one based on algebraic decision diagrams and one on a variant of Shannon expansions. Finally, we implement our decision procedure and evaluate it on more than 10,000 formulas. Despite the generality, our implementation has comparable performance with the state-of-the-art M2L-STR solvers.

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Implementation and Application of Automata : 18th international conference, CIAA 2013, Halifax, NS, Canada, July 16-19, 2013, proceedings

Citations

Monadic second-order logic on finite sequences

References

Monadic second-order logic on finite sequences

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