Showing papers on "Continuous automaton published in 1971"

A context-free language which is not acceptable by a probabilistic automaton

Abstract: A linear context-free language which is not acceptable by a finite probabilistic automaton is given, and it is shown that the family of stochastic languages is not closed under concatenation and homomorphism.

A Two-Way Automaton with Fewer States than Any Equivalent One-Way Automaton

Abstract: This correspondence presents an example of a two-way automaton which has significantly fewer states than any one-way automaton accepting the same set of tapes. Thus, in this particular case, memory space can be saved by using a two-way automaton. This savings in space, however, is accompanied by an increase in recognition time.

Analysis for an Effective Operation of a General Automaton: Recursive Methods Applied to a Graph Model

Abstract: With many there is a general agreement that the problems arising from large and complex systems in society are interdisciplinary in nature and that pending solutions require contributions from all concerned who are willing to view the problems in full perspective There is a need for the development of a general theory which can serve as a basis for establishing theoretical concepts fundamental to the various disciplines Such a theory could then be used directly in the modeling and studying of a specific physical system or system component In [1], we first identified a component of general system and treated it as a general automaton That work concluded with a graph model for a general automaton The natural extension presented here is the development and application of recursive methods for determining properties of these graphs that reflect the effective operation of the general automaton The recursive methods provide a means of studying a component of such a system by a computer The key r

Automaton structure preserving morphisms with applications to decomposition and simulation

Abstract: Publisher Summary This chapter discusses automaton structure preserving morphisms with applications to decomposition and simulation. The relation that expresses the preservation of structure from a structured automaton M to a structured automaton M' is called a structure preserving morphism. Such a morphism preserves not only the transition and output functions of the abstract automaton but also the manner in which these functions arise out of the local coordinate functions in its structured representation. The chapter describes the truly homomorphic preservation of the transition function and the reduction of complexity for measures relevant to the simulation of structured automata. The introduction of the structure morphism concept makes possible improved prediction of the relative complexities of an automaton and its simulators. As the number of possible simulators is controlled by the simulation criterion, more efficient search methods can be developed using structure morphisms.

Connectivity and separation in automata

Abstract: Publisher Summary This chapter presents several characteristics of connectedness and of separation in automata and discusses their relationships to other connectivity properties and to the basic structure of automata. An automaton is finite only if its set of states is finite. A primary of a nonempty finite automaton is a maximal singly generated subautomaton. The union and the intersection of subautomata of A are themselves subautomata of A. The chapter illustrates a method for finding the minimal separated subautomata of a finite automaton and explains its use in determining the homomorphisms, endomorphisms, isomorphisms, and automorphisms of finite automata. The separated parts of an automaton can be regarded as unrelated automata with the same input alphabet. Every nonempty automaton is made entirely of blocks. Many problems are profitably reducible to the natural building blocks. Two blocks of a nonempty automaton are either identical or disjoint. A nonempty subautomaton C of A is separated only if C is the union of blocks of A.

Theorems on additive automata

Abstract: Publisher Summary This chapter discusses theorems on additive automata. The theory of linear automata is well developed, and many works have appeared on this topic. To every given automaton, there belongs a unique minimal one, which is a homomorpic image of it. The minimal automaton, belonging to a linear automaton over a field K, is again a linear automaton over the same field. The chapter discusses whether the minimal automaton belonging to an additive automaton is again additive with the same operator sets. Many well-known results on linear automata can be generalized to additive automata. The chapter describes the necessary and sufficient conditions for the (H,K)-realizability of an automaton M.