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Learning to Complement Büchi Automata

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10747))

Abstract

Complementing Büchi automata is an intriguing and intensively studied problem. Complementation suffers from a theoretical super-exponential complexity. From an applied point of view, however, there is no reason to assume that the target language is more complex than the source language. The chance that the smallest representation of a complement language is (much) smaller or (much) larger than the representation of its source should be the same; after all, complementing twice is an empty operation. With this insight, we study the use of learning for complementation. We use a recent learning approach for FDFAs, families of DFAs, that can be used to represent \(\omega \)-regular languages, as a basis for our complementation technique. As a surprising result, it has proven beneficial not to learn an FDFA that represents the complement language of a Büchi automaton (or the language itself, as complementing FDFAs is cheap), but to use it as an intermediate construction in the learning cycle. While the FDFA is refined in every step, the target is an associated Büchi automaton that underestimates the language of a conjecture FDFA. We have implemented our approach and compared it on benchmarks against the algorithms provided in GOAL. The complement automata we produce for large Büchi automata are generally smaller, which makes them more valuable for applications like model checking. Our approach has also been faster in 98% of the cases. Finally we compare the advantages we gain by the novel techniques with advantages provided by the high level optimisations implemented in the state-of-the-art tool SPOT.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Yong Li, Andrea Turrini & Lijun Zhang

  2. University of Chinese Academy of Sciences, Beijing, China

    Yong Li & Lijun Zhang

  3. University of Liverpool, Liverpool, UK

    Sven Schewe

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  1. Yong Li
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  2. Andrea Turrini
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  4. Sven Schewe
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Correspondence to Lijun Zhang .

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Editors and Affiliations

  1. University of Texas , Austin, Texas, USA

    Isil Dillig

  2. University of California , Los Angeles, California, USA

    Jens Palsberg

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Li, Y., Turrini, A., Zhang, L., Schewe, S. (2018). Learning to Complement Büchi Automata. In: Dillig, I., Palsberg, J. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2018. Lecture Notes in Computer Science(), vol 10747. Springer, Cham. https://doi.org/10.1007/978-3-319-73721-8_15

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