Automata with finite congruence lattices
In this paper we prove that if the congruence lattice of an automaton A is finite then the endomorphism semigroup E(A) of A is finite. Moreover, if A is commutative then A is A-finite. We prove that if 3 ≤ |A| then a commutative automaton A is simple if and only if it is a cyclic permutation automat...
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| Format: | Article |
| Published: |
2007
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| Series: | Acta cybernetica
18 No. 1 |
| Kulcsszavak: | Számítástechnika, Kibernetika |
| Subjects: | |
| Online Access: | http://acta.bibl.u-szeged.hu/12808 |
| Summary: | In this paper we prove that if the congruence lattice of an automaton A is finite then the endomorphism semigroup E(A) of A is finite. Moreover, if A is commutative then A is A-finite. We prove that if 3 ≤ |A| then a commutative automaton A is simple if and only if it is a cyclic permutation automaton of prime order. We also give some results concerning cyclic, strongly connected and strongly trap-connected automata. |
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| Physical Description: | 155-165 |
| ISSN: | 0324-721X |