1. On the encoding and solving partial information games
- Author
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Amoussou-Guenou , Yackolley, Baarir , Souhein, Potop-Butucaru , Maria, Sznajder , Nathalie, Tible , Leo, Tixeuil , Sébastien, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Networks and Performance Analysis (NPA), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Modélisation et Vérification (MoVe), Laboratory of Information, Network and Communication Sciences (LINCS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Mines-Télécom [Paris] (IMT)-Sorbonne Université (SU), Middleware on the Move (MIMOVE), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), LIP6, Sorbonne Université, CNRS, UMR 7606, LINCS, CEA Paris Saclay, Sorbonne Université, Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Networks and Performance Analysis ( NPA ), Laboratoire d'Informatique de Paris 6 ( LIP6 ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Centre National de la Recherche Scientifique ( CNRS ), Modélisation et Vérification ( MoVe ), Laboratory of Information, Network and Communication Sciences ( LINCS ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut Mines-Télécom [Paris], Middleware on the Move ( MIMOVE ), and Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria )
- Subjects
Computer Science::Computer Science and Game Theory ,[ INFO.INFO-DC ] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC] ,[INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL] ,[ INFO.INFO-FL ] Computer Science [cs]/Formal Languages and Automata Theory [cs.FL] ,[ INFO.INFO-RB ] Computer Science [cs]/Robotics [cs.RO] ,Partial information games ,Mobile robots 31 ,[INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO] ,Memoryless games ,[INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC] - Abstract
In this paper we address partial information games restricted to memoryless strategies.Our contribution is threefold. First, we prove that for partial information games, deciding the existence of memoryless strategies is NP-complete, even for games with only reachability objectives. %This result is interesting in itself since in the case of games with total information it is already proven that memory is not necessary to win the game. The second contribution of this paper is a SAT/SMT-based encoding of a partial information game altogether with the correctness proof of this encoding. Finally, we apply our methodology to automatically synthesize strategies for oblivious mobile robots. We first prove that synthesizing memoryless strategies is equivalent to providing a distributed protocol for the robots. Then, we use an SMT-solver to synthesize strategies for the gathering problem in a particular configuration ($SP_4$), open case in distributed computing theory for more than a decade. Interestingly, our work is the first that combines two-player games theory and SMT-solvers in the context of mobile robots with promising results and therefore it is highly valuable for distributed computing theory where a broad class of open problems are still to be investigated.
- Published
- 2018