Abstract
Arbitrary finite automata are decomposed into their major substructures, the primaries. Several characterizations of homomorphisms, endomorphisms, isomorphisms, and automorphisms of arbitrary finite automata are presented via reduction to the primaries of the automata. Various characterizations of these transition-preserving functions on singly generated automata are presented and are used as a basis for the reduction. Estimates on the number of functions of each type are given.
- 1 ARBIB, M.A. Automaton automorphisms. Inform. Contr.; to appear.Google Scholar
- 2 BARNES, B. Groups of automorphisms and sets of equivalence classes of input for automata. J. ACM 12, 4 (Oct. 1965), 561-565. Google Scholar
- 3 BAVEL, Z. On the structure and automorphisms of finite automata. Rep. 192, Dept. d Computer Science, U. of Illinois, Urbana, Oct. 1965.Google Scholar
- 4 BAVEL, Z., AND MULLER, D.E. Reversibility in monadic algebras and automata. 1965 IEEE Conf. Rec. on Switching Circuit Theory and Logical Design, Oct. 1965, pp. 242-247.Google Scholar
- 5 BAYER, R. Automorphism groups and quotients of'strongly connected automata and monadic algebras. 1966 IEEE Conf. Rec. on Switching and Automata Theory, Oct. 1966, pp. 282-297.Google Scholar
- 6 FLECK, A.C. Isomorphism groups of automata. J. ACM 9, 4 (Oct. 1962), 469-476. Google Scholar
- 7 --. On the automorphism group of an automaton. J. ACM 12, 4 (Oct. 1965), 566-560. Google Scholar
- 8 OEHMKE, R. H. On the structure of an automaton and its input semigroup. J. ACM 10, 4 (Oct. 1963), 521-525. Google Scholar
- 9 TRAUTH, C. A., JR. Group-type automata. J. ACM 18, 1 (Jan. 1966), 170--175. Google Scholar
- 10 WEEG, G.P. The structure of an automaton and its operation preserving transforraation group. J. ACM 9, 3 (July 1962), 345-349. Google Scholar
- 11 --. The automorphism group of the direct product of strongly related automata. J. ACM 12, 2 (April 1965), 187-195. Google Scholar
- 12 SHULT, E.E. Private communication.Google Scholar
Index Terms
- Structure and Transition-Preserving Functions of Finite Automata
Recommendations
Oblivious two-way finite automata: Decidability and complexity
We investigate the descriptional complexity and decidability of obliviousness for two-way finite automata. In particular, we consider the simulation of two-way deterministic finite automata (2DFAs) by oblivious 2DFAs, the simulation of oblivious 2DFAs ...
Complementing two-way finite automata
We study the relationship between the sizes of two-way finite automata accepting a language and its complement. In the deterministic case, for a given automaton (2dfa) with n states, we build an automaton accepting the complement with at most 4n states, ...
Comments