1. On Cardinality of the Group of Weak Fuzzy Automaton Isomorphisms
- Author
-
S. R. Chaudhari and S. S. Dhure
- Subjects
Discrete mathematics ,Block cellular automaton ,TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES ,Mathematics::General Mathematics ,Computer science ,Powerset construction ,Continuous automaton ,Timed automaton ,Pushdown automaton ,Büchi automaton ,Nonlinear Sciences::Cellular Automata and Lattice Gases ,Reversible cellular automaton ,Deterministic pushdown automaton ,Nondeterministic finite automaton with ε-moves ,ComputingMethodologies_PATTERNRECOGNITION ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Elementary cellular automaton ,Deterministic automaton ,Probabilistic automaton ,Two-way deterministic finite automaton ,ComputingMethodologies_GENERAL ,Nondeterministic finite automaton ,Isomorphism ,Algorithm ,Computer Science::Formal Languages and Automata Theory - Abstract
Recent studies on fuzzy automata are influenced by algebraic techniques to tackle issues like reduction, minimization and their languages. Fuzzy automaton homomorphism is one such majorally discussed technique. This paper is concerned with the group of (weak) fuzzy automaton automorphisms and constructions of all (weak) fuzzy automaton automorphisms over arbitrary fuzzy automaton. It is shown that (1) every arbitrary fuzzy automaton is decomposed into distinct primaries, (2) primaries are maximal singly generated fuzzy automata and (3) every weak fuzzy automaton homomorphism on an arbitrary fuzzy automaton is uniquely determined into weak fuzzy automaton homomorphisms on all its primaries. Therefore, the discussion begun over strongly connected fuzzy automaton and continue constructions as well as characterizations of (weak) fuzzy automaton homomorphisms, isomorphisms, endomorphisms and automorphisms sequentially over perfect fuzzy automaton, singly generated fuzzy automaton and primaries of fuzzy automaton. Finally, it is obtained that the group of weak fuzzy automaton automorphisms and its cardinality over arbitrary fuzzy automaton.
- Published
- 2013