Games Where You Can Play Optimally with Arena-Independent Finite Memory
For decades, two-player (antagonistic) games on graphs have been a framework of choice for many important problems in theoretical computer science. A notorious one is controller synthesis, which can be rephrased through the game-theoretic metaphor as the quest for a winning strategy of the system in...
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| Vydáno v: | Logical methods in computer science Ročník 18, Issue 1 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Logical Methods in Computer Science Association
17.01.2022
Logical Methods in Computer Science e.V |
| Témata: | |
| ISSN: | 1860-5974, 1860-5974 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | For decades, two-player (antagonistic) games on graphs have been a framework
of choice for many important problems in theoretical computer science. A
notorious one is controller synthesis, which can be rephrased through the
game-theoretic metaphor as the quest for a winning strategy of the system in a
game against its antagonistic environment. Depending on the specification,
optimal strategies might be simple or quite complex, for example having to use
(possibly infinite) memory. Hence, research strives to understand which
settings allow for simple strategies.
In 2005, Gimbert and Zielonka provided a complete characterization of
preference relations (a formal framework to model specifications and game
objectives) that admit memoryless optimal strategies for both players. In the
last fifteen years however, practical applications have driven the community
toward games with complex or multiple objectives, where memory -- finite or
infinite -- is almost always required. Despite much effort, the exact frontiers
of the class of preference relations that admit finite-memory optimal
strategies still elude us.
In this work, we establish a complete characterization of preference
relations that admit optimal strategies using arena-independent finite memory,
generalizing the work of Gimbert and Zielonka to the finite-memory case. We
also prove an equivalent to their celebrated corollary of great practical
interest: if both players have optimal (arena-independent-)finite-memory
strategies in all one-player games, then it is also the case in all two-player
games. Finally, we pinpoint the boundaries of our results with regard to the
literature: our work completely covers the case of arena-independent memory
(e.g., multiple parity objectives, lower- and upper-bounded energy objectives),
and paves the way to the arena-dependent case (e.g., multiple lower-bounded
energy objectives). |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.46298/lmcs-18(1:11)2022 |