Parity games and automata for game logic

Parity games and automata for game logic

Hansen, H.H. (TU Delft Energy and Industry)
Kupke, Clemens (University of Strathclyde)
Marti, Johannes (University of Strathclyde)
Venema, Yde (Universiteit van Amsterdam)

2018

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.

http://resolver.tudelft.nl/uuid:caac78d7-d837-4327-bf6e-d8ff5e69499c

https://doi.org/10.1007/978-3-319-73579-5_8

Springer

9783319735788

Dynamic Logic. New Trends and Applications - 1st International Workshop, DALI 2017, Proceedings, 10669 LNCS

1st International Workshop on Dynamic Logic, DALI 2017, 2017-09-23 → 2017-09-24, Brasilia, Brazil

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 0302-9743, 10669 LNCS

Institutional Repository

conference paper

© 2018 H.H. Hansen, Clemens Kupke, Johannes Marti, Yde Venema