Parity games and automata for game logic

Hansen, Helle Hvid and Kupke, Clemens and Marti, Johannes and Venema, Yde; Madeira, Alexandre and Benevides, Mário, eds. (2018) Parity games and automata for game logic. In: Dynamic Logic. New Trends and Applications. Lecture Notes in Computer Science . Springer, Cham, pp. 115-132. (https://doi.org/10.1007/978-3-319-73579-5_8)

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Abstract

Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone μ-calculus, which in turn is expressively equivalent to monotone modal automata. Parity games and automata are important tools for dealing with the combinatorial complexity of nested fixpoints in modal fixpoint logics, such as the modal μ-calculus. In this paper, we (1) discuss the semantics a of game logic over neighbourhood structures in terms of parity games, and (2) use these games to obtain an automata-theoretic characterisation of the fragment of the monotone μ-calculus that corresponds to game logic. Our proof makes extensive use of structures that we call syntax graphs that combine the ease-of-use of syntax trees of formulas with the flexibility and succinctness of automata. They are essentially a graph-based view of the alternating tree automata that were introduced by Wilke in the study of modal μ-calculus.

  • Item type:Book Section
    ID code:62083
    Dates:
    Date
    Event
    3 January 2018
    Published
    3 January 2018
    Published Online
    24 July 2017
    Accepted
    Keywords:logic, automata theory, game theory, combinatorial problems, graph theory, Electronic computers. Computer science, Computational Theory and Mathematics, Computational Mathematics
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:19 Oct 2017 09:55
    Last modified:01 Apr 2022 02:49
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/62083
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