Some algorithms for equivalent transformation of nondeterministic finite automata

In this paper we consider algorithms which allow one to combine several states of a nondeterministic finite automaton into one state. Along with the algorithms for combining states, we adduce one more algorithm for the equivalent transformation of a non-deterministic finite automaton, namely, an algorithm for adding cycles. Problems under consideration imply the development of robust computer programs.     

Once more about the state-minimization of the nondeterministic finite automata

In this paper we consider the corrected version of the algorithm of the state-minimization for the nondeterministic finite automata: we correct here a mistake of the previous paper, where the same problem was considered.     

A new algorithm of the state-minimization for the nondeterministic finite automata

The problem of the state-minimization for the nondeterministic finite Rabin-Scott’s automata is considered. A new algorithm for this problem is obtained. The obtained algorithm has the exponential effectiveness, like the earlier-known algorithms for this problem. But each of previous algorithms amounts to the search of minimum generative system for local reaction of equal automaton of canonical form, and unlike them, we use in this paper two special functions, marking states of the given automaton.     

On the equivalence of stationary and finite-nonstationary nondeterministic automata

The synthesis problem for a generalized stationary nondeterministic automaton equivalent to an arbitrary given generalized finite-nonstationary nondeterministic automation is solved. A synthesis algorithm is described.     

Shortest directing words of nondeterministic directable automata

In this paper, we will survey several results on the shortest directing words of various types of nondeterministic directable automata.¹     

Finitely nonstationary nondeterministic automata with random input

Properties of generalized finitely nonstationary nondeterministic automata with an additional random input over a Boolean lattice are considered which are related to the definition of the class of languages represented by such automaton models. New notions of an elementary nondeterministic automatic structure with a random input, of a generalized finitely nonstationary nondeterministic automaton with a random input, of the generalized mapping induced by such an automaton, and of a generalized language represented by such an automaton are introduced. A number of statements substantiating synthesis for any given generalized finitely nonstationary nondeterministic automaton with a random input of an abstract probabilistic finite automaton equivalent to the given one relative to the represented generalized language probabilistic language of the stationary abstract probabilistic finite automaton. The number of states of the synthesized probabilistic automaton is estimated and a synthesis algorithm is developed in detail and illustrated by an example.     

格值有限自动机的乘积

初步建立了格值有限自动机的乘积理论.引入了格值变换半群,研究了格值有限自动机在各种乘积情形下的转移函数性质,讨论了各种乘积之间的覆盖关系,为进一步研究量子自动机的乘积理论奠定基础.     

Edge-minimization of non-deterministic finite automata

In this paper we consider non-deterministic finite Rabin-Scott’s automata. We use a special structure to describe all the possible edges of non-deterministic finite automaton defining the given regular language. Such structure can be used for solving various problems of finite automata theory. One of these problems is edge-minimization of non-deterministic automata. As we have not touched this problem before, we obtain here two versions of the algorithm for solving this problem to continue previous series of articles.     

Codification schemes and finite automata

This paper is a note on how Information Theory and Codification Theory are helpful in the computational design of both communication protocols and strategy sets in the framework of finitely repeated games played by bounded rational agents. More precisely, we show the usefulness of both theories to improve the existing automata bounds on the work of Neyman (1998) Finitely repeated games with finite automata, Mathematics of Operations Research, 23 (3), 513–552.     

Minimization algorithm of fuzzy finite automata

In this paper, a class of fuzzy finite automata corresponding to the Mealy type of ordinary automata is formulated, and also two types of statewise equivalence relations are introduced. From the equivalence relations, a minimal form is defined and a minimization algorithm of the Mealy type of fuzzy finite automata is obtained.     

On the finite series expansion of multivariate characteristic functions

Three theorems are obtained that relate the asymptotic behavior of a distribution function with the behavior of its characteristic function at the origin. These theorems generalize one dimensional results that have been obtained by the author and by others.     

Some more on the finite automata

Some new problems of the theory of the finite automata are considered. Applying the finite automata in various tasks of the formal languages theory is observed. Special proof of Kleene’s theorem is obtained. This proof is used for the defining the star-height of the finite automaton. The properties of the last object are considered. The star-height of the finite automaton is used for reformulating the star-height problem of regular expressions for finite automata. The method of the reduction of the star-height problem to the task of making special finite automaton is obtained. This reformulating can help to solve the star-height problem by new way.     

An intersection problem for finite automata

A finite automaton with state space S and alphabet A can be thought of as a directed graph with vertex set S such that for each vertex t ϵ S the edges leaving t are in one-to-one correspondence with A. Motivated by a problem in logic, we propose a problem about intersections of languages accepted by finite automata and give some partial results.     

Two-person repeated games with finite automata

We study two-person repeated games in which a player with a restricted set of strategies plays against an unrestricted player. An exogenously given bound on the complexity of strategies, which is measured by the size of the smallest automata that implement them, gives rise to a restriction on strategies available to a player.  We examine the asymptotic behavior of the set of equilibrium payoffs as the bound on the strategic complexity of the restricted player tends to infinity, but sufficiently slowly. Results from the study of zero sum case provide the individually rational payoff levels. Received February 1997/revised version March 2000     

On an expansion of Almansi type

We obtain an expansion of Almansi type for functions satisfying the equation Δ _λ ^m u = 0, where Δ _λ = λ ₁ ? ²/?x ₁ ² + … + λ _n ? ²/?x _n ² and λ _k ≠ 0.