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Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

Author

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  • Theodore Andronikos

    (Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece)

  • Alla Sirokofskich

    (Department of History and Philosophy of Sciences, National and Kapodistrian University of Athens, Athens 15771, Greece)

  • Kalliopi Kastampolidou

    (Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece)

  • Magdalini Varvouzou

    (Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece)

  • Konstantinos Giannakis

    (Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece)

  • Alexander Singh

    (Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece)

Abstract

The meticulous study of finite automata has produced many important and useful results. Automata are simple yet efficient finite state machines that can be utilized in a plethora of situations. It comes, therefore, as no surprise that they have been used in classic game theory in order to model players and their actions. Game theory has recently been influenced by ideas from the field of quantum computation. As a result, quantum versions of classic games have already been introduced and studied. The P Q penny flip game is a famous quantum game introduced by Meyer in 1999. In this paper, we investigate all possible finite games that can be played between the two players Q and Picard of the original P Q game. For this purpose, we establish a rigorous connection between finite automata and the P Q game along with all its possible variations. Starting from the automaton that corresponds to the original game, we construct more elaborate automata for certain extensions of the game, before finally presenting a semiautomaton that captures the intrinsic behavior of all possible variants of the P Q game. What this means is that, from the semiautomaton in question, by setting appropriate initial and accepting states, one can construct deterministic automata able to capture every possible finite game that can be played between the two players Q and Picard. Moreover, we introduce the new concepts of a winning automaton and complete automaton for either player.

Suggested Citation

  • Theodore Andronikos & Alla Sirokofskich & Kalliopi Kastampolidou & Magdalini Varvouzou & Konstantinos Giannakis & Alexander Singh, 2018. "Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game," Mathematics, MDPI, vol. 6(2), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:2:p:20-:d:129842
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    References listed on IDEAS

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    Cited by:

    1. Kalliopi Kastampolidou & Christos Papalitsas & Theodore Andronikos, 2022. "The Distributed Kolkata Paise Restaurant Game," Games, MDPI, vol. 13(3), pages 1-21, April.

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