# On the encoding and solving partial information games

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.
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https://hal.archives-ouvertes.fr/hal-01790508
Contributor : Maria Potop-Butucaru <>
Submitted on : Sunday, May 20, 2018 - 10:55:20 AM
Last modification on : Wednesday, June 24, 2020 - 4:19:52 PM
Long-term archiving on: : Tuesday, August 21, 2018 - 5:20:43 PM

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• HAL Id : hal-01790508, version 1

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Yackolley Amoussou-Guenou, Souheib Baarir, Maria Potop-Butucaru, Nathalie Sznajder, Leo Tible, et al.. On the encoding and solving partial information games. [Research Report] LIP6, Sorbonne Université, CNRS, UMR 7606; LINCS; CEA Paris Saclay; Sorbonne Université. 2018. ⟨hal-01790508⟩

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