Parity games and automata for game logic

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

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

2 Citations (Scopus)
13 Downloads (Pure)

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.

Original languageEnglish
Title of host publicationDynamic Logic. New Trends and Applications - 1st International Workshop, DALI 2017, Proceedings
PublisherSpringer
Pages115-132
Number of pages18
Volume10669 LNCS
ISBN (Print)9783319735788
DOIs
Publication statusPublished - 2018
Event1st International Workshop on Dynamic Logic, DALI 2017 - Brasilia, Brazil
Duration: 23 Sep 201724 Sep 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10669 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference1st International Workshop on Dynamic Logic, DALI 2017
CountryBrazil
CityBrasilia
Period23/09/1724/09/17

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