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 |
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Keywords
- logic
- automata theory
- game theory
- combinatorial problems
- graph theory
Cite this
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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 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 -