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Asian Symposium on Programming Languages and Systems

APLAS 2019: Programming Languages and Systems pp 447–467Cite as

Simulations in Rank-Based Büchi Automata Complementation

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11893))

Abstract

Complementation of Büchi automata is an essential technique used in some approaches for termination analysis of programs. The long search for an optimal complementation construction climaxed with the work of Schewe, who proposed a worst-case optimal rank-based procedure that generates complements of a size matching the theoretical lower bound of \((0.76n)^n\), modulo a polynomial factor of \(\mathcal {O}(n^2)\). Although worst-case optimal, the procedure in many cases produces automata that are unnecessarily large. In this paper, we propose several ways of how to use the direct and delayed simulation relations to reduce the size of the automaton obtained in the rank-based complementation procedure. Our techniques are based on either (i) ignoring macrostates that cannot be used for accepting a word in the complement or (ii) saturating macrostates with simulation-smaller states, in order to decrease their total number. We experimentally showed that our techniques can indeed considerably decrease the size of the output of the complementation.

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Notes

  1. 1.

    Note that our basic definitions slightly differs from the ones in Sect. 2.3 of [33]. This is because of a typo in [33]; indeed, if the procedure from [33] is implemented as is, the output does not accept the complement (there might be a macrostate (S, O, f) where S contains accepting states and O is empty, and, therefore, the whole macrostate is accepting, which is wrong).

  2. 2.

    https://github.com/vhavlena/ba-complement .

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Acknowledgement

We thank the anonymous reviewers for their helpful comments on how to improve the exposition in this paper. This work was supported by the Ministry of Science and Technology of Taiwan project 106-2221-E-001-009-MY3 the Czech Science Foundation project 19-24397S, the FIT BUT internal project FIT-S-17-4014, and The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project IT4Innovations excellence in science—LQ1602.

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Authors and Affiliations

  1. Academia Sinica, Taipei, Taiwan

    Yu-Fang Chen

  2. FIT, IT4I Centre of Excellence, Brno University of Technology, Brno, Czech Republic

    Vojtěch Havlena & Ondřej Lengál

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  1. Yu-Fang Chen
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  2. Vojtěch Havlena
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Correspondence to Ondřej Lengál .

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  1. University of Kaiserslautern, Kaiserslautern, Germany

    Anthony Widjaja Lin

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Chen, YF., Havlena, V., Lengál, O. (2019). Simulations in Rank-Based Büchi Automata Complementation. In: Lin, A. (eds) Programming Languages and Systems. APLAS 2019. Lecture Notes in Computer Science(), vol 11893. Springer, Cham. https://doi.org/10.1007/978-3-030-34175-6_23

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