| Institute of Informatics>>> Acta Cybernetica>>> Past Issues>>> Volume 18, Number 1, 2007>>> |
 Magyarul
|
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
Available electronic editions: PDF.
Note that full text is available only for papers that are at least 3 years old. For more recent papers only the first page of the paper is provided.
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.}
}