Nested Antichains for WS1S

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My contributions

1. While I was not the author of the main idea, I helped shaped the final decision procedure and came up with several significant optimisations of the process.
2. I was the main developer of the decision procedure.
3. I run the experiments and interpreted the results.

Abstract

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.

Cite us

FIEDOR Tomáš, HOLÍK Lukáš, LENGÁL Ondřej and VOJNAR Tomáš. Nested Antichains for WS1S. In: Proceedings of TACAS'15. Lecture Notes in Computer Science, vol. 9035. Heidelberg: Springer Verlag, 2015, pp. 658-674. ISBN 978-3-662-46680-3.