Publication detail

Nested Antichains for WS1S

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/"
}