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22
Tiling Semigroups
 11TH ICALP, LECTURE NOTES IN COMPUTER SCIENCE 199
, 1999
"... It has recently been shown how to construct an inverse semigroup from any tiling: a construction having applications in Ktheoretical gaplabelling. In this paper, we provide the categorical basis for this construction in terms of an appropriate group acting partially and without fixed points on ..."
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Cited by 36 (10 self)
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It has recently been shown how to construct an inverse semigroup from any tiling: a construction having applications in Ktheoretical gaplabelling. In this paper, we provide the categorical basis for this construction in terms of an appropriate group acting partially and without fixed points on an inverse category associated with the tiling.
Recognizable Sets with Multiplicities in the Tropical Semiring
, 1988
"... The last ten years saw the emergence of some results about recognizable subsets of a free monoid with multiplicities in the MinPlus semiring. An interesting aspect of this theoretical body is that its discovery was motivated throughout by applications such as the finite power property, Eggan's ..."
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Cited by 32 (1 self)
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The last ten years saw the emergence of some results about recognizable subsets of a free monoid with multiplicities in the MinPlus semiring. An interesting aspect of this theoretical body is that its discovery was motivated throughout by applications such as the finite power property, Eggan's classical star height problem and the measure of the nondeterministic complexity of finite automata. We review here these results, their applications and point out some open problems. 1 Introduction One of the richest extensions of finite automaton theory is obtained by associating multiplicities to words, edges and states. Perhaps the most intuitive appearence of this concept is obtained by counting for every word the number of successful paths spelling it in a (nondeterministic) finite automaton. This is motivated by the formalization of ambiguity in a finite automaton and leads to the theory of recognizable subsets of a free monoid with multiplicities in the semiring of natural numbers. This...
Tropical Semirings
"... this paper is to present other semirings that occur in theoretical computer science. These semirings were baptized tropical semirings by Dominique Perrin in honour of the pioneering work of our brazilian colleague and friend Imre Simon, but are also commonly known as (min; +)semirings ..."
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Cited by 24 (0 self)
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this paper is to present other semirings that occur in theoretical computer science. These semirings were baptized tropical semirings by Dominique Perrin in honour of the pioneering work of our brazilian colleague and friend Imre Simon, but are also commonly known as (min; +)semirings
On the Burnside problem for Semigroups of Matrices in the (max,+) Algebra
, 1996
"... We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max,+)algebra (that is, the semiring (R[ f\Gamma1g; max; +)), and also for semigroups of (max,+)linear projective maps with rational entries. An application to the estimation of the Lyapuno ..."
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Cited by 11 (2 self)
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We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max,+)algebra (that is, the semiring (R[ f\Gamma1g; max; +)), and also for semigroups of (max,+)linear projective maps with rational entries. An application to the estimation of the Lyapunov exponent of certain products of random matrices is also discussed. 1. Introduction The "(max,+)algebra" is a traditional name for the semiring (R[f\Gamma1g; max; +), denoted Rmax in the sequel. This is a particular example of idempotent semiring (that is a semiring whose additive law satisfies a \Phi a = a), also known as dioid [17, 18, 2]. This algebraic structure has been popularized by its applications to Graph Theory and Operations Research [17, 8]. Linear operators in this algebra are central in HamiltonJacobi theory and in the study of exponential asymptotics [33]. The study of automata and semigroups of matrices over the analogous "tropical" semiring (N [ f+1g;min;+) has been ...
The Topological Approach to the Limitedness Problem on Distance Automata
, 1998
"... this paper, we present the topological approach to the limitedness problem on distance automata. Our techniques has been improved so that the Brown's result is no longer needed. The main mathematical tools used are the local structure theory for nite semigroup [13] and some basic topological i ..."
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Cited by 8 (1 self)
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this paper, we present the topological approach to the limitedness problem on distance automata. Our techniques has been improved so that the Brown's result is no longer needed. The main mathematical tools used are the local structure theory for nite semigroup [13] and some basic topological ideas. Most of the technical results in this paper except Lemma 3.9 and Lemma 3.10 were obtained in ([14], [15]). Besides for the sake of completeness, we include all the proofs because many of them have been reworked for better presentations
Factorisation forests for infinite words Application to countable scattered linear
"... orderings ..."
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Semigroups with idempotent stabilizers and application to automata theory
 Int. J. of Alg. and Comput
, 1991
"... Nous prouvons que tout semigroupe fini est quotient d’un semigroupe fini dans lequel les stabilisateurs droits satisfont les identités x = x2 et xy = xyx. Ce résultat a plusieurs conséquences. Tout d’abord, nous l’utilisons, en même temps qu’un résultat de I. Simon sur les congruences de chemin ..."
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Cited by 4 (0 self)
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Nous prouvons que tout semigroupe fini est quotient d’un semigroupe fini dans lequel les stabilisateurs droits satisfont les identités x = x2 et xy = xyx. Ce résultat a plusieurs conséquences. Tout d’abord, nous l’utilisons, en même temps qu’un résultat de I. Simon sur les congruences de chemins, pour obtenir une preuve purement algébrique d’un théorème profond de McNaughton sur les mots infinis. Puis, nous donnons une preuve algébrique d’un théorème de Brown sur des conditions de finitude pour les semigroupes. We show that every finite semigroup is a quotient of a finite semigroup in which every right stabilizer satisfies the identities x = x2 and xy = xyx. This result has several consequences. We first use it together with a result of I. Simon on congruences on paths to obtain a purely algebraic proof of a deep theorem of McNaughton on infinite words. Next, we give an algebraic proof of a theorem of Brown on a finiteness condition for semigroups. 1
Some Results on the DotDepth Hierarchy
, 1992
"... : In this paper we pursue the study of the decidability of the dotdepth hierarchy. We give an e#ective lower bound for the dotdepth of an aperiodic monoid. The main tool for this is the study of a certain operation on varieties of finite monoids in terms of Mal'cev product. We also prove the ..."
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Cited by 4 (1 self)
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: In this paper we pursue the study of the decidability of the dotdepth hierarchy. We give an e#ective lower bound for the dotdepth of an aperiodic monoid. The main tool for this is the study of a certain operation on varieties of finite monoids in terms of Mal'cev product. We also prove the equality of two decidable varieties which were known to contain all dotdepth two monoids. Finally, we restrict our attention to inverse monoids, and we prove that the class of inverse dotdepth two monoids is locally finite. In this paper we pursue the study of the dotdepth hierarchy, a hierarchy of starfree (i.e. recognizable aperiodic) languages with connections to finite monoid theory, formal logic (Thomas [30]) and computational complexity (Barrington and Therien [1]). The dotdepth hierarchy was first introduced by Brzozowski and Cohen [3] in 1971 and was studied by numerous authors since. It consists in a strictly increasing sequence of classes of starfree languages whose union is the c...
On Semigroups of Matrices in the (max,+) Algebra
, 1994
"... We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max; +)algebra (that is, the semiring (R[ f\Gamma1g; max; +)), and also for semigroups of (max; +)linear projective maps with rational entries. An application to the estimation of the Lyap ..."
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Cited by 2 (1 self)
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We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max; +)algebra (that is, the semiring (R[ f\Gamma1g; max; +)), and also for semigroups of (max; +)linear projective maps with rational entries. An application to the estimation of the Lyapunov exponent of certain products of random matrices is also discussed.