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On the topological structure of a finitely generated semigroup of matrices. (English) Zbl 0646.20056

From the author’s introduction: The aim of this paper is to show that there is an algorithm to compute a certain homomorphic image of the topological closure of a finitely generated semigroup of matrices over \(M_ 1\), where \(M_ 1=({\mathbb{N}}\cup \{\omega,\infty \},\min.,+,\infty,0)\). Hence we obtain another proof that the limitedness problem is decidable. In addition, a faster decision algorithm can be derived. In this paper, we also extend the result to show that there is an algorithm to compute a certain homomorphic image of the topological closure of a finitely generated semigroup of matrices over \(M_ 2\) where \(M_ 2=({\mathbb{N}}\cup \{\infty \},+,.,0,1)\) and \(\omega\) is the point at infinity.
Reviewer: Ph.Das

MSC:

20M35 Semigroups in automata theory, linguistics, etc.
20M05 Free semigroups, generators and relations, word problems
20M20 Semigroups of transformations, relations, partitions, etc.
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References:

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