Parity games and automata for game logic

Helle Hvid Hansen, Clemens Kupke, Johannes Marti, Yde Venema

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

2 Citations (Scopus)

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.
LanguageEnglish
Title of host publicationDynamic Logic. New Trends and Applications
Subtitle of host publicationFirst International Workshop, DALI 2017, Brasilia, Brazil, September 23-24, 2017, Proceedings
EditorsAlexandre Madeira, Mário Benevides
Place of PublicationCham
PublisherSpringer
Pages115-132
Number of pages18
DOIs
Publication statusE-pub ahead of print - 3 Jan 2018

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume10669
ISSN (Print)0302-9743

Fingerprint

Parity
Automata
Semantics
Game
Logic
μ-calculus
Fixpoint
Monotone
Fragment
Combinatorial Complexity
Tree Automata
Graph in graph theory
Flexibility

Keywords

  • logic
  • automata theory
  • game theory
  • combinatorial problems
  • graph theory

Cite this

Hansen, H. H., Kupke, C., Marti, J., & Venema, Y. (2018). Parity games and automata for game logic. In A. Madeira, & M. Benevides (Eds.), Dynamic Logic. New Trends and Applications: First International Workshop, DALI 2017, Brasilia, Brazil, September 23-24, 2017, Proceedings (pp. 115-132). (Lecture Notes in Computer Science; Vol. 10669). Cham: Springer. https://doi.org/10.1007/978-3-319-73579-5_8
Hansen, Helle Hvid ; Kupke, Clemens ; Marti, Johannes ; Venema, Yde . / Parity games and automata for game logic. Dynamic Logic. New Trends and Applications: First International Workshop, DALI 2017, Brasilia, Brazil, September 23-24, 2017, Proceedings. editor / Alexandre Madeira ; Mário Benevides. Cham : Springer, 2018. pp. 115-132 (Lecture Notes in Computer Science).
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Hansen, HH, Kupke, C, Marti, J & Venema, Y 2018, Parity games and automata for game logic. in A Madeira & M Benevides (eds), Dynamic Logic. New Trends and Applications: First International Workshop, DALI 2017, Brasilia, Brazil, September 23-24, 2017, Proceedings. Lecture Notes in Computer Science, vol. 10669, Springer, Cham, pp. 115-132. https://doi.org/10.1007/978-3-319-73579-5_8

Parity games and automata for game logic. / Hansen, Helle Hvid; Kupke, Clemens; Marti, Johannes ; Venema, Yde .

Dynamic Logic. New Trends and Applications: First International Workshop, DALI 2017, Brasilia, Brazil, September 23-24, 2017, Proceedings. ed. / Alexandre Madeira; Mário Benevides. Cham : Springer, 2018. p. 115-132 (Lecture Notes in Computer Science; Vol. 10669).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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Hansen HH, Kupke C, Marti J, Venema Y. Parity games and automata for game logic. In Madeira A, Benevides M, editors, Dynamic Logic. New Trends and Applications: First International Workshop, DALI 2017, Brasilia, Brazil, September 23-24, 2017, Proceedings. Cham: Springer. 2018. p. 115-132. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-319-73579-5_8