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Pseudovarieties of Ordered Completely Regular Semigroups
This paper is a contribution to the theory of finite semigroups and their classification in pseudovarieties, which is motivated by its connections...
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Semigroup Actions on Sets and the Burnside Ring
In this paper we discuss some enlargements of the category of sets with semigroup actions and equivariant functions. We show that these enlarged...
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Automatic semigroups and Bruck-Reilly extensions
The interaction of automatic semigroups and Bruck-Reilly extensions is studied. It is proved that every automatic Bruck-Reilly extension has an...
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Fixed points of endomorphisms over special confluent rewriting systems
Cayley graphs of monoids defined through special confluent rewriting systems are known to be hyperbolic metric spaces which admit a compact...
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Unambiguous Automata
We give a new presentation of two results concerning synchronized automata. The first one gives a linear bound on the synchronization delay of...
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Solid codes and the uniform density of fd-domains
By means of further investigation of solid codes, the problem “Is every fd-domain uniformly dense” proposed by Yuqi Guo, C. M. Reis and G. Thierrin...
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Completely Simple Semigroups, Lie Algebras, and the Road Coloring Problem
Consider a semigroup generated by matrices associated with an edge-coloring of a strongly connected, aperiodic digraph. We call the semigroup...
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Automata and Square Complexes
We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex...
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Semigroups and the Generalized Road Coloring Problem
The road coloring problem has been open for some 25 years. This paper shows how algebraic methods, specifically semigroup theory, can be used to...
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Notions of automaticity in semigroups
We will investigate various possible notions of automaticity in semigroups. We point out that it makes a difference which side we choose for...
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Some remarks on the structure of free automata
In this paper we define automata-linearly independence. An automaton M has a basis B iff M is free provided that we assume that the action of S on X × S ...
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Small and large automata
In this paper we define small and large(or big) automata. We investigate some algebraic properties associated with them
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