Lazy Automata Techniques for WS1S

  • Tomáš Fiedor
  • Lukáš Holík
  • Petr Janků
  • Ondřej LengálEmail author
  • Tomáš Vojnar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10205)


We present a new decision procedure for the logic WS1S. It originates from the classical approach, which first builds an automaton accepting all models of a formula and then tests whether its language is empty. The main novelty is to test the emptiness on the fly, while constructing a symbolic, term-based representation of the automaton, and prune the constructed state space from parts irrelevant to the test. The pruning is done by a generalization of two techniques used in antichain-based language inclusion and universality checking of finite automata: subsumption and early termination. The richer structure of the WS1S decision problem allows us, however, to elaborate on these techniques in novel ways. Our experiments show that the proposed approach can in many cases significantly outperform the classical decision procedure (implemented in the Mona tool) as well as recently proposed alternatives.


Decision Procedure Free Variable Atomic Formula Finite Automaton Automaton State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank the anonymous reviewers for their helpful comments on how to improve the presentation in this paper. This work was supported by the Czech Science Foundation (projects 16-17538S and 16-24707Y), the BUT FIT project FIT-S-17-4014, and the IT4IXS: IT4Innovations Excellence in Science project (LQ1602).


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Tomáš Fiedor
    • 1
  • Lukáš Holík
    • 1
  • Petr Janků
    • 1
  • Ondřej Lengál
    • 1
    • 2
    Email author
  • Tomáš Vojnar
    • 1
  1. 1.FITBrno University of Technology, IT4Innovations Centre of ExcellenceBrnoCzech Republic
  2. 2.Institute of Information ScienceAcademia SinicaTaipeiTaiwan

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