Nested Antichains for WS1S

  • Tomáš Fiedor
  • Lukáš Holík
  • Ondřej Lengál
  • Tomáš Vojnar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9035)


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 by several orders of magnitude.


Decision Procedure Symbolic Representation Tree Automaton Deterministic Automaton Nondeterministic Automaton 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Tomáš Fiedor
    • 1
  • Lukáš Holík
    • 1
  • Ondřej Lengál
    • 1
  • Tomáš Vojnar
    • 1
  1. 1.IT4Innovations Centre of ExcellenceFIT, Brno University of TechnologyBrnoCzech Republic

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