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

1
Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece
2
Department of History and Philosophy of Sciences, National and Kapodistrian University of Athens, Athens 15771, Greece
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Authors to whom correspondence should be addressed.
Mathematics 2018, 6(2), 20; https://doi.org/10.3390/math6020020
Received: 29 October 2017 / Revised: 17 January 2018 / Accepted: 26 January 2018 / Published: 1 February 2018
(This article belongs to the Special Issue Mathematical Game Theory)
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. View Full-Text
Keywords: finite automata; games; PQ penny flip game; game variants; winning sequences finite automata; games; PQ penny flip game; game variants; winning sequences
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MDPI and ACS Style

Andronikos, T.; Sirokofskich, A.; Kastampolidou, K.; Varvouzou, M.; Giannakis, K.; Singh, A. Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game. Mathematics 2018, 6, 20. https://doi.org/10.3390/math6020020

AMA Style

Andronikos T, Sirokofskich A, Kastampolidou K, Varvouzou M, Giannakis K, Singh A. Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game. Mathematics. 2018; 6(2):20. https://doi.org/10.3390/math6020020

Chicago/Turabian Style

Andronikos, Theodore, Alla Sirokofskich, Kalliopi Kastampolidou, Magdalini Varvouzou, Konstantinos Giannakis, and Alexander Singh. 2018. "Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game" Mathematics 6, no. 2: 20. https://doi.org/10.3390/math6020020

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