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

2017 ◽  
Author(s):  
Theodore Andronikos ◽  
Alla Sirokofskich ◽  
Kalliopi Kastampolidou ◽  
Magdalini Varvouzou ◽  
Konstantinos Giannakis ◽  
...  
Keyword(s):  
Game Theory ◽  
Quantum Computation ◽  
Finite Automata ◽  
State Machines ◽  
Quantum Game ◽  
Finite Games ◽  
New Concepts ◽  
Finite Game ◽  
Finite State ◽  
Deterministic Automata

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.

REPRESENTATIONS AND IDENTIFICATIONS OF STRUCTURAL AND MOTION STATE CHARACTERISTICS OF MECHANISMS WITH VARIABLE TOPOLOGIES

2006 ◽  
Vol 30 (1) ◽  
pp. 19-40 ◽  
Author(s):  
Hong-Sen Yan ◽  
Chin-Hsing Kuo
Keyword(s):  
Topological Structure ◽  
Topological Analysis ◽  
State Machines ◽  
Matrix Representations ◽  
Motion State ◽  
New Concepts ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Finite State ◽  
State Graphs

A mechanism that encounters a certain changes in its topological structure during operation is called a mechanism with variable topologies (MVT). This paper is developed for the structural and motion state representations and identifications of MVTs. For representing the topological structures of MVTs, a set of methods including graph and matrix representations is proposed. For representing the motion state characteristics of MVTs, the idea of finite-state machines is employed via the state tables and state graphs. And, two new concepts, the topological homomorphism and motion homomorphism, are proposed for the identifications of structural and motion state characteristics of MVTs. The results of this work provide a logical foundation for the topological analysis and synthesis of mechanisms with variable topologies.

scholarly journals Finite State Testing and Syntax Testing

2012 ◽  
Vol 3 (1) ◽  
pp. 48-54
Author(s):  
Amandeep Singh ◽  
Harmanjit Singh
Keyword(s):  
Practical Importance ◽  
Finite State Machines ◽  
Model Systems ◽  
Modular Organization ◽  
State Testing ◽  
State Machines ◽  
New Concepts ◽  
Finite State ◽  
New Applications ◽  
Advanced Computer

This paper is concerned with the testing of the software which is being developed in a structured way. The advantages which accrue from a well-structured or modular organization of software depend upon an ability to independently test a module well before the full development of all the modules with which it communicates. This paper describes techniques (Finite State Testing & Syntax Testing) which effectively test various applications. With advanced computer technology, systems are getting larger to fulfill more complicated tasks, however, they are also becoming less reliable. Consequently, testing is an indispensable part of system design and implementation; yet it has proved to be a formidable task for complex systems. This motivates the study of testing finite state machines to ensure the correct functioning of systems and to discover aspects of their behavior. Finite state machines are widely used to model systems in diverse areas, including sequential circuits, certain types of programs, and, more recently, communication protocols. In a testing problem we have a machine about which we lack some information; we would like to deduce this information by providing a sequence of inputs to the machine and observing the outputs produced. Because of its practical importance and theoretical interest, the problem of testing finite state machines have been studied in different areas and at various times. Some old problems which had been open for decades were resolved recently, new concepts and more intriguing problems from new applications emerge. This paper reviews the fundamental problems in testing finite state machines and techniques for solving these problems, tracing progress in the area from its inception to the present and the state of the art. In addition, this paper covers syntax testing which is also called grammar based testing technique for testing various applications where the input data can be described formally.

scholarly journals Quantum Conditional Strategies and Automata for Prisoners’ Dilemmata under the EWL Scheme

2019 ◽  
Vol 9 (13) ◽  
pp. 2635 ◽  
Author(s):  
Konstantinos Giannakis ◽  
Georgia Theocharopoulou ◽  
Christos Papalitsas ◽  
Sofia Fanarioti ◽  
Theodore Andronikos
Keyword(s):  
Game Theory ◽  
Finite Automata ◽  
State Machines ◽  
Conditional Strategy ◽  
Abstract Machines ◽  
Quantum Finite Automata ◽  
Quantum Version ◽  
Important Field ◽  
Classical Game ◽  
Classical Game Theory

Classical game theory is an important field with a long tradition of useful results. Recently, the quantum versions of classical games, such as the prisoner’s dilemma (PD), have attracted a lot of attention. This game variant can be considered as a specific type of game where the player’s actions and strategies are formed using notions from quantum computation. Similarly, state machines, and specifically finite automata, have also been under constant and thorough study for plenty of reasons. The quantum analogues of these abstract machines, like the quantum finite automata, have been studied extensively. In this work, we examine well-known conditional strategies that have been studied within the framework of the classical repeated PD game. Then, we try to associate these strategies to proper quantum finite automata that receive them as inputs and recognize them with a probability of 1, achieving some interesting results. We also study the quantum version of PD under the Eisert–Wilkens–Lewenstein scheme, proposing a novel conditional strategy for the repeated version of this game.

More on Minimizing Finite Automata with Errors — Nondeterministic Machines

2017 ◽  
Vol 28 (03) ◽  
pp. 229-245
Author(s):  
Markus Holzer ◽  
Sebastian Jakobi
Keyword(s):  
Finite Automata ◽  
Finite State Machines ◽  
State Machines ◽  
Minimization Problems ◽  
Nondeterministic Finite Automata ◽  
Significant Difference ◽  
Finite State ◽  
Error Profiles ◽  
Equivalence Problems

We continue our research on minimization problems and related problems for automata w.r.t. to different error profiles, now considering nondeterministic finite automata (NFAs) as inputs. Here the error profiles are almost-equivalence and E-equivalence. We show that the minimization problems and their underlying equivalence problems become PSPACE-complete in most cases. The obtained results nicely fit to the known ones on ordinary NFA minimization, and show a significant difference to the previously obtained results on deterministic finite state machines.

scholarly journals Multitiered Nonlinear Morphology Using Multitape Finite Automata: A Case Study on Syriac and Arabic

2000 ◽  
Vol 26 (1) ◽  
pp. 77-105 ◽  
Author(s):  
George Anton Kiraz
Keyword(s):  
Finite Automata ◽  
State Machines ◽  
Surface Form ◽  
Lexical Representations ◽  
Tier Ii ◽  
Autosegmental Phonology ◽  
Finite State ◽  
Rewrite Rules ◽  
Main Components

This paper presents a computational model for nonlinear morphology with illustrations from Syriac and Arabic. The model is a multitiered one in that it allows for multiple lexical representations corresponding to the multiple tiers of autosegmental phonology. The model consists of three main components: (i) a lexicon, which is made of sublexica, with each sublexicon representing lexical material from a specific tier, (ii) a rewrite rules component that maps multiple lexical representations into one surface form and vice versa, and (iii) a morphotactic component that employs regular grammars. The system is finite-state in that lexica and rules can be represented by multitape finite-state machines.

scholarly journals A Class of 2-Head Finite Automata for Linear Languages

Triangle ◽  
2018 ◽  
pp. 89
Author(s):  
Benedek Nagy
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
State Machines ◽  
Deterministic Automata ◽  
Even Linear Languages

Both deterministic and non-deterministic nite state machines (automata) recognize regular languages exactly. Now we extend these machines using two heads to characterize even-linear and linear languages. The heads move in opposite directions in these automata. For even-linear languages, deterministic automata have the same eciency as non-deterministic ones, but for the general case (linear languages) only the non-deterministic version is sucient. We compare our automata to other two-head automata as well.

scholarly journals Quantum Conditional Strategies for Prisoners' Dilemmata Under the Ewl Scheme

2019 ◽  
Author(s):  
Konstantinos Giannakis ◽  
Georgia Theocharopoulou ◽  
Christos Papalitsas ◽  
Sofia Fanarioti ◽  
Theodore Andronikos
Keyword(s):  
Game Theory ◽  
Prisoner's Dilemma ◽  
Finite Automata ◽  
Prisoner’S Dilemma ◽  
State Machines ◽  
Conditional Strategy ◽  
Abstract Machines ◽  
Quantum Finite Automata ◽  
Quantum Version ◽  
Important Field

Classic game theory is an important field with a long tradition of useful results. Recently, the quantum versions of classical games, such as the Prisoner's Dilemma (PD), have attracted a lot of attention. Similarly, state machines and specifically finite automata have also been under constant and thorough study for plenty of reasons. The quantum analogues of these abstract machines, like the quantum finite automata, have been studied extensively. In this work, we examine some well-known game conditional strategies that have been studied within the framework of the repeated PD game. Then, we try to associate these strategies to proper quantum finite automata that receive them as inputs and recognize them with probability 1, achieving some interesting results. We also study the quantum version of PD under the Eisert-Wilkens-Lewenstein scheme, proposing a novel conditional strategy for the repeated version of this game.

scholarly journals One-Time Nondeterministic Computations

2019 ◽  
Vol 30 (06n07) ◽  
pp. 1069-1089
Author(s):  
Markus Holzer ◽  
Martin Kutrib
Keyword(s):  
Finite Automata ◽  
State Machines ◽  
Computational Power ◽  
Deterministic Finite Automaton ◽  
Worst Case ◽  
Trade Offs ◽  
Finite State ◽  
Nondeterministic State ◽  
Pushdown Automata ◽  
Limited Nondeterminism

We introduce the concept of one-time nondeterminism as a new kind of limited nondeterminism for finite state machines and pushdown automata. Roughly speaking, one-time nondeterminism means that at the outset the computation is nondeterministic, but whenever it performs a guess, this guess is fixed for the rest of the computation. We characterize the computational power of one-time nondeterministic finite automata (OTNFAs) and one-time nondeterministic pushdown devices. Moreover, we study the descriptional complexity of these machines. For instance, we show that for an [Formula: see text]-state OTNFA with a sole nondeterministic state, that is nondeterministic for only one input symbol, [Formula: see text] states are sufficient and necessary in the worst case for an equivalent deterministic finite automaton. In case of pushdown automata, the conversion of a nondeterministic to a one-time nondeterministic as well as the conversion of a one-time nondeterministic to a deterministic one turn out to be non-recursive, that is, the trade-offs in size cannot be bounded by any recursive function.

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