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.
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Item type: Book Section ID code: 62083 Dates: DateEvent3 January 2018Published3 January 2018Published Online24 July 2017AcceptedSubjects: 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: 11 Nov 2024 15:11 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/62083