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On the PSPACE-completeness of Peg Duotaire and other Peg-Jumping Games

Authors Davide Bilò , Luciano Gualà , Stefano Leucci , Guido Proietti , Mirko Rossi

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Davide Bilò
  • Dipartimento di Scienze Umanistiche e Sociali, University of Sassari, Italy.
Luciano Gualà
  • Dipartimento di Ingegneria dell'Impresa, University of Rome "Tor Vergata", Italy.
Stefano Leucci
  • Institute of Theoretical Computer Science, ETH Zürich, Switzerland.
Guido Proietti
  • Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, University of L'Aquila, Italy, and Istituto di Analisi dei Sistemi ed Informatica, CNR, Roma, Italy.
Mirko Rossi
  • Dipartimento di Ingegneria dell'Impresa, University of Rome "Tor Vergata", Italy.

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Davide Bilò, Luciano Gualà, Stefano Leucci, Guido Proietti, and Mirko Rossi. On the PSPACE-completeness of Peg Duotaire and other Peg-Jumping Games. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.FUN.2018.8

Abstract

Peg Duotaire is a two-player version of the classical puzzle called Peg Solitaire. Players take turns making peg-jumping moves, and the first player which is left without available moves loses the game. Peg Duotaire has been studied from a combinatorial point of view and two versions of the game have been considered, namely the single- and the multi-hop variant. On the other hand, understanding the computational complexity of the game is explicitly mentioned as an open problem in the literature. We close this problem and prove that both versions of the game are PSPACE-complete. We also prove the PSPACE-completeness of other peg-jumping games where two players control pegs of different colors.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • peg duotaire
  • pspace-completeness
  • peg solitaire
  • two-player games

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