Nested Antichains for WS1S

Nested Antichains for WS1S

Paper in proceedings (conference paper)

We propose a novel approach for coping with alternating quantification as the main source of nonelementary complexity of deciding WS1S formulae. Our approach is applicable within the state-of-the-art automata-based WS1S decision procedure implemented, e.g., in MONA. The way in which the standard decision procedure processes quantifiers involves determinization, with its worst case exponential complexity, for every quantifier alternation in the prefix of a formula. Our algorithm avoids building the deterministic automata-instead, it constructs only those of their states needed for (dis)proving validity of the formula. It uses a symbolic representation of the states, which have a deeply nested structure stemming from the repeated implicit subset construction, and prunes the search space by a nested subsumption relation, a generalisation of the one used by the so-called antichain algorithms for handling non-deterministic automata. We have obtained encouraging experimental results, in some cases outperforming MONA by several orders of magnitude.

We propose a novel approach for coping with alternating quantification as the main source of nonelementary complexity of deciding WS1S formulae. Our approach is applicable within the state-of-the-art automata-based WS1S decision procedure implemented, e.g., in MONA. The way in which the standard decision procedure processes quantifiers involves determinization, with its worst case exponential complexity, for every quantifier alternation in the prefix of a formula. Our algorithm avoids building the deterministic automata-instead, it constructs only those of their states needed for (dis)proving validity of the formula. It uses a symbolic representation of the states, which have a deeply nested structure stemming from the repeated implicit subset construction, and prunes the search space by a nested subsumption relation, a generalisation of the one used by the so-called antichain algorithms for handling non-deterministic automata. We have obtained encouraging experimental results, in some cases outperforming MONA by several orders of magnitude.

antichains
WS1S
finite automata
subsumption
nondeterministic automata

antichains
WS1S
finite automata
subsumption
nondeterministic automata

FIEDOR, T.; HOLÍK, L.; LENGÁL, O.; VOJNAR, T.

2016

13.04.2015

Springer Verlag

Heidelberg

978-3-662-46680-3

Proceedings of TACAS'15

Lecture Notes in Computer Science

9035

658

674

17

http://dx.doi.org/10.1007/978-3-662-46681-0_59

http://hdl.handle.net/