### Abstract

Language | English |
---|---|

Title of host publication | Dynamic Logic. New Trends and Applications |

Subtitle of host publication | First International Workshop, DALI 2017, Brasilia, Brazil, September 23-24, 2017, Proceedings |

Editors | Alexandre Madeira, Mário Benevides |

Place of Publication | Cham |

Publisher | Springer |

Pages | 115-132 |

Number of pages | 18 |

DOIs | |

Publication status | E-pub ahead of print - 3 Jan 2018 |

### Publication series

Name | Lecture Notes in Computer Science |
---|---|

Publisher | Springer |

Volume | 10669 |

ISSN (Print) | 0302-9743 |

### Fingerprint

### Keywords

- logic
- automata theory
- game theory
- combinatorial problems
- graph theory

### Cite this

*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

}

*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 .

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Parity games and automata for game logic

AU - Hansen, Helle Hvid

AU - Kupke, Clemens

AU - Marti, Johannes

AU - Venema, Yde

PY - 2018/1/3

Y1 - 2018/1/3

N2 - 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.

AB - 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.

KW - logic

KW - automata theory

KW - game theory

KW - combinatorial problems

KW - graph theory

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

U2 - 10.1007/978-3-319-73579-5_8

DO - 10.1007/978-3-319-73579-5_8

M3 - Conference contribution book

T3 - Lecture Notes in Computer Science

SP - 115

EP - 132

BT - Dynamic Logic. New Trends and Applications

A2 - Madeira, Alexandre

A2 - Benevides, Mário

PB - Springer

CY - Cham

ER -