Book ChapterDOI
Connectivity and separation in automata
Zamir Bavel
- pp 255-274
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TLDR
This chapter illustrates a method for finding the minimal separated subautomata of a finite automaton and explains its use in determining the homomorphicisms, endomorphisms, isomorphisms and automorphisms of finite 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.read more
Citations
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Journal ArticleDOI
A fuzzy topology associated with a fuzzy finite state machine
TL;DR: The concepts of separation of fuzzy subsystems and connectedness of fuzzy finite state machines are developed and some results on connectedness and weak connectedness are obtained.
Journal ArticleDOI
A topology for automata: A note
Wagish Shukla,Arun K. Srivastava +1 more
TL;DR: It is shown that many automata-theoretic concepts, e.g., separation, connectivity, retrievability, strong connectivity, etc., have standard topological analogs under this topology and many results concerning these concepts are direct consequences of this observation.
References
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Journal ArticleDOI
Structure and Transition-Preserving Functions of Finite Automata
TL;DR: Arbitrary finite automata are decomposed into their major substructures, the primaries, and various characterizations of these transition-preserving functions on singly generated Automata are presented and are used as a basis for the reduction.
Journal ArticleDOI
Group-Type Automata
TL;DR: The purpose is to investigate the input structure of automata which have a group-like character and the class of perfect automata investigated by Fleck and Weeg is a proper subclass of those considered here.
Proceedings ArticleDOI
Automorphism groups and quotients of strongly connected automata and monadic algebras
TL;DR: Applications to decomposition theory, in particular to the problem of factoring out identical parallel front components, are given and a generalization of the major parts of the theory to infinite strongly connected monadic algebras is obtained.
Journal ArticleDOI
Connectivity and Reversibility in Automata
Zamir Bavel,David E. Muller +1 more
TL;DR: It is shown that in the case of finite automata five of these properties are equivalent, and the reverse, Rev(A), of an automaton A is defined and its relationship to A is studied.