Publication Details
Nested Antichains for WS1S
Holík Lukáš, doc. Mgr., Ph.D. (DITS FIT BUT)
Lengál Ondřej, Ing., Ph.D. (DITS FIT BUT)
Vojnar Tomáš, prof. Ing., Ph.D. (DITS FIT BUT)
antichains
WS1S
finite automata
subsumption
nondeterministic automata
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.
@INPROCEEDINGS{FITPUB10790,
author = "Tom\'{a}\v{s} Fiedor and Luk\'{a}\v{s} Hol\'{i}k and Ond\v{r}ej Leng\'{a}l and Tom\'{a}\v{s} Vojnar",
title = "Nested Antichains for WS1S",
pages = "658--674",
booktitle = "Proceedings of TACAS'15",
series = "Lecture Notes in Computer Science",
volume = 9035,
year = 2015,
location = "Heidelberg, DE",
publisher = "Springer Verlag",
ISBN = "978-3-662-46680-3",
doi = "10.1007/978-3-662-46681-0\_59",
language = "english",
url = "https://www.fit.vut.cz/research/publication/10790"
}