arXiv subjects

Anup Basil Mathew

Publications and source records attributed to Anup Basil Mathew.

4 recordsLinked to original sources

arXiv2016

Hierarchical Information and the Synthesis of Distributed Strategies

Infinite games with imperfect information are known to be undecidable unless the information flow is severely restricted. One fundamental decidable case occurs when there is a total ordering among players, such that each player has access to all the information that the following ones receive. In this paper we consider variations of this hierarchy principle for synchronous games with perfect recall, and identify new decidable classes for which the distributed synthesis problem is solvable with finite-state strategies. In particular, we show that decidability is maintained when the information hierarchy may change along the play, or when transient phases without hierarchical information are allowed. Finally, we interpret our result in terms of distributed system architectures.

cs.GT↗

arXiv2016

A Retraction Theorem for Distributed Synthesis

We present a general theorem for distributed synthesis problems in coordination games with $ω$-regular objectives of the form: If there exists a winning strategy for the coalition, then there exists an "essential" winning strategy, that is obtained by a retraction of the given one. In general, this does not lead to finite-state winning strategies, but when the knowledge of agents remains bounded, we can solve the synthesis problem. Our study is carried out in a setting where objectives are expressed in terms of events that may \emph{not} be observable. This is natural in games of imperfect information, rather than the common assumption that objectives are expressed in terms of events that are observable to all agents. We characterise decidable distributed synthesis problems in terms of finiteness of knowledge states and finite congruence classes induced by them.

cs.DC↗

arXiv2015

Infinite games with finite knowledge gaps

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning strategies can be constructed effectively without restricting the direction of information flow. Instead, our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play. We show that it is decidable whether a given game satisfies the condition, and prove tight complexity bounds for the strategy synthesis problem under $ω$-regular winning conditions given by parity automata.

cs.GT↗

arXiv2014

Games with recurring certainty

Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players become uncertain about the current state of the game, and this uncertainty lasts forever. Here we consider games where the players attain certainty about the current state over and over again along any play. For finite-state games, we note that this kind of recurring certainty implies a stronger condition of periodic certainty, that is, the events of state certainty ultimately occur at uniform, regular intervals. We show that it is decidable whether a given game presents recurring certainty, and that, if so, the problem of synthesising coordination strategies under w-regular winning conditions is solvable.

cs.LO↗