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FIEDOR, T. HOLÍK, L. LENGÁL, O. VOJNAR, T.
Original Title
Nested Antichains for WS1S
Type
journal article in Web of Science
Language
English
Original 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 generalization of the one used by the so-called antichain algorithms for handling nondeterministic automata. We have obtained encouraging experimental results, in some cases outperforming Mona, and some of the other recently proposed approaches, by several orders of magnitude.
Keywords
antichains WS1S finite automata subsumption
Authors
FIEDOR, T.; HOLÍK, L.; LENGÁL, O.; VOJNAR, T.
Released
1. 1. 2019
ISBN
0001-5903
Periodical
Acta Informatica
Year of study
56
Number
3
State
Federal Republic of Germany
Pages from
205
Pages to
228
Pages count
24
URL
https://www.fit.vut.cz/research/publication/11889/
BibTex
@article{BUT161577, author="Tomáš {Fiedor} and Lukáš {Holík} and Ondřej {Lengál} and Tomáš {Vojnar}", title="Nested Antichains for WS1S", journal="Acta Informatica", year="2019", volume="56", number="3", pages="205--228", doi="10.1007/s00236-018-0331-z", issn="0001-5903", url="https://www.fit.vut.cz/research/publication/11889/" }