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# Automata with Finite Congruence Lattices

### Abstract (in LaTeX format)

In this paper we prove that if the congruence lattice of an automaton $\mathbf{A}$ is finite then the endomorphism semigroup $E(\mathbf{A})$ of $\mathbf{A}$ is finite. Moreover, if $\mathbf{A}$ is commutative then $\mathbf{A}$ is A-finite. We prove that if $3\leq|A|$ then a commutative automaton $\mathbf{A}$ 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.

### Full text

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### BibTeX entry

@ARTICLE{Babcsanyi:2007:ActaCybernetica,
author = {Istv\'an Babcs\'anyi},
title = {Automata with Finite Congruence Lattices},
journal = {Acta Cybernetica},
year = {2007},
volume = {18},
number = {1},
pages = {155--165},
abstract = {In this paper we prove that if the congruence lattice of an automaton $\mathbf{A}$ is finite then the endomorphism semigroup $E(\mathbf{A})$ of $\mathbf{A}$ is finite. Moreover, if $\mathbf{A}$ is commutative then $\mathbf{A}$ is A-finite. We prove that if $3\leq|A|$ then a commutative automaton $\mathbf{A}$ 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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