Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 29 October 2017 / Approved: 30 October 2017 / Online: 30 October 2017 (04:29:12 CET)

A peer-reviewed article of this Preprint also exists.

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. 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.

Journal reference: Mathematics 2018, 6, 20
DOI: 10.3390/math6020020

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 PQ 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 PQ game. For this purpose we establish a rigorous connection between finite automata and the PQ 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 PQ 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.

Subject Areas

finite automata; games; PQ penny flip game; game variants; winning sequences

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