Exploring the boundary of half-positionality

Bianco, Alessandro; Faella, Marco; Mogavero, Fabio; Murano, Aniello

doi:10.1007/s10472-011-9250-1

Cited by 8 publications

(10 citation statements)

References 13 publications

(32 reference statements)

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“…Albeit close, this is distinct from the half-positional determinacy result from [BFMM11, Theorem 3], which gives sufficient conditions about a winning condition for a player to admit memoryless optimal strategies on every two-player arena -in Theorem 3.8, we give a necessary and sufficient condition for a player to admit UFM strategies on his oneplayer arenas only. The sufficient conditions from [BFMM11] (strong monotony and strong concavity) imply M triv -monotony and M triv -selectivity, but not the other way around. Given a preference relation, it is possible for a player to have UFM strategies on his one-player arenas, but not on all two-player arenas: e.g., the example used in [BFMM11,Lemma 15].…”

Section: Resultsmentioning

confidence: 98%

“…The sufficient conditions from [BFMM11] (strong monotony and strong concavity) imply M triv -monotony and M triv -selectivity, but not the other way around. Given a preference relation, it is possible for a player to have UFM strategies on his one-player arenas, but not on all two-player arenas: e.g., the example used in [BFMM11,Lemma 15]. In such an example, Theorem 3.8 could be applied, but not the result from [BFMM11].…”

Section: Resultsmentioning

confidence: 98%

“…Given a preference relation, it is possible for a player to have UFM strategies on his one-player arenas, but not on all two-player arenas: e.g., the example used in [BFMM11,Lemma 15]. In such an example, Theorem 3.8 could be applied, but not the result from [BFMM11].…”

Section: Resultsmentioning

confidence: 99%

“…Second, Bianco et al establish sufficient (and relaxed) conditions to ensure the existence of UML strategies for one player, in two-player games, in [BFMM11]: it would be interesting to study the corresponding problem in the finite-memory case. Indeed, in many games where infinite memory is needed, it is only the case for one of the players (e.g., [VCD + 15, CHJ05, BHRR19]) and such conditions could thus prove useful.…”

Section: Discussionmentioning

confidence: 99%

“…Following this observation, a lot of effort has been put into understanding which games admit memoryless optimal strategies, and in identifying the exact frontiers of memoryless determinacy. Let us mention, non-exhaustively, works by Gimbert and Zielonka [GZ04,GZ05] (culminating in a complete characterization), Aminof and Rubin [AR17] (through the prism of first-cycle games), and Kopczyński [Kop06] and Bianco et al [BFMM11] (half-positional determinacy). All these advances were built by identifying the common underlying mechanisms in ad hoc proofs for specific classes of games, and generalizing them to wide classes (e.g., the first-cycle games of Aminof and Rubin are inspired by the seminal paper of Ehrenfeucht and Mycielski on mean-payoff games [EM79]).…”

Section: Introductionmentioning

confidence: 99%

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Games Where You Can Play Optimally with Arena-Independent Finite Memory

Bouyer¹,

Roux²,

Oualhadj³

et al. 2022

Logical Methods in Computer Science

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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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Section: Resultsmentioning

confidence: 98%

Section: Resultsmentioning

confidence: 98%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Games Where You Can Play Optimally with Arena-Independent Finite Memory

Bouyer¹,

Roux²,

Oualhadj³

et al. 2022

Logical Methods in Computer Science

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First-cycle games

Aminof

Rubin

2017

Information and Computation

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First-cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of the edges (or nodes) forming this cycle. These games are intimately connected with classic infinite-duration games such as parity and mean-payoff games. We initiate the study of FCGs in their own right, as well as formalise and investigate the connection between FCGs and certain infinite-duration games.We establish that (for efficiently computable Y ) the problem of solving FCGs is Pspace-complete; we show that the memory required to win FCGs is, in general, Θ(n)! (where n is the number of nodes in the graph); and we give a full characterisation of those properties Y for which all FCGs are memoryless determined.We formalise the connection between FCGs and certain infinite-duration games and prove that strategies transfer between them. Using the machinery of FCGs, we provide a recipe that can be used to very easily deduce that many infinite-duration games, e.g., mean-payoff, parity, and energy games, are memoryless determined.

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Positional ω-regular languages

Casares,

Ohlmann

2024

Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science

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Exploring the boundary of half-positionality

Cited by 8 publications

References 13 publications

Games Where You Can Play Optimally with Arena-Independent Finite Memory

Games Where You Can Play Optimally with Arena-Independent Finite Memory

First-cycle games

Positional ω-regular languages

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