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ω-automaton
About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.
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TL;DR: This paper studies implementation of cooperative payoffs in finitely repeated games when players implement their strategies by finite automata of big sizes and offers a domain of definition of the smallest automaton which includes previous domains in the literature.
Abstract: This paper studies implementation of cooperative payoffs in finitely repeated games when players implement their strategies by finite automata of big sizes. Specifically, we analyze how much we have to depart from fully rational behavior to achieve the Folk Theorem payoffs, i.e., which are the maximum bounds on automata complexity which yield cooperative behavior in long but not infinite interactions. To this end we present a new approach to the implementation of the mixed strategy equilibrium paths leading to cooperation. The novelty is to offer a new construction of the set of the pure strategies which belong to the mixed strategy equilibrium. Thus, we consider the subset of strategies which is characterized by both the complexity of the finite automata and the entropy associated to the underlying coordination process. The equilibrium play consists of both a communication phase and the play of a cycle which depends on the chosen message. The communication set is designed by tools of Information Theory. Moreover, the characterization of this set is given by the complexity of the weaker player that implements the equilibrium play. We offer a domain of definition of the smallest automaton which includes previous domains in the literature.
1 citations
01 Jan 1995
TL;DR: A number of examples of hybrid systems and quantum automata consisting of interacting networks of classical systems and automata are presented and some relationships between them are pointed out.
Abstract: Let H denote an algebra of input symbols or events. If X is the state space for a system, then one can form the space R of observations of X. Under suitable conditions, both X and R are H-modules. Loosely speaking, the formal systems studied in this paper consists of a bialgebra H describing the input symbols and two H-modules describing the states and observations of the system. Finite automata and input-output systems are concerned with commutative R, while quantum systems, such as quantum automata, are concerned with non-commutative R arising from Hermitian operators on the state space. Of special interest are those systems consisting of interacting networks of classical systems and automata. These types of systems have become known as hybrid systems and are examples of formal systems with commutative R. In this paper, we present a number of examples of hybrid systems and quantum automata and point out some relationships between them. This is a preliminary announcement: a detailed exposition, including proofs, will appear elsewhere.
1 citations
TL;DR: The compactness of the state spaces with respect to the metric is discussed and this leads to the theorem: A stationary, causal and finitely observable discrete lime system can be represented by and only by finite automata.
Abstract: This paper deals with the characterization problem or finite state automata. Firstly, two examples of automata are presented, one indicating the existence of some specific class of automata which is on the boundary between finite and infinite automata, and the other as a counterexample to a condition which has been speculated to characterize the finite state automaton class. Secondly, a metric called causal metric is defined for discrete time systems, and the concept of causality of general time systems is topologically characterized for discrete cases. Based on the causal metric another metric is defined on the state spaces of discrete time systems. The compactness of the state spaces with respect to the metric is discussed and this leads us to the theorem: A stationary, causal and finitely observable discrete lime system can be represented by and only by finite automata.
1 citations
TL;DR: This paper investigates automata whose state sets and sets of output symbols are endowed with algebraic structures of hypergraphs and solves the problem of concrete characterization of universal hypergraphic automata.
Abstract: In the paper we investigate automata whose state sets and sets of output symbols are endowed with algebraic structures of hypergraphs. Universal hypergraphic automata are universally attracting objects in the category of such automata. The main result is a solving of the problem of concrete characterization of universal hypergraphic automata.
1 citations
11 Mar 2011
TL;DR: This paper discusses about 1-QFA and 2-Q FA and their drawbacks, and introduces an algorithm by implementing 1-way quantum finite k-counter automata (1-QFk-CA) with multiple scanning of the input string to improve the power of QFAs.
Abstract: The 1-way quantum finite automata and 2-way quantum finite automata are the first ever developed quantum automatons. But they suffer from many disadvantages which make them less powerful and impracticable. To remove these drawbacks there are many ways to modify and aggrandize the quantum finite automatons. Including 1-counter with 1-way QFA significantly improve its power. Likely quantum finite automata with quantum and classical states (QCFA) and 2-way quantum finite 1-counter automata (2-QF1-CA) are the quintessence of these modifications. In our paper we first discuss about 1-QFA and 2-QFA and their drawbacks. In the section IV we introduce an algorithm by implementing 1-way quantum finite k-counter automata (1-QFk-CA). Then we discuss another algorithm by implementing quantum finite 1-counter automata (QF1-CA) with multiple scanning of the input string. These algorithms improve the power of QFAs.
1 citations