Results 1  10
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16
Semigroup and ring theoretical methods in probability
, 2004
"... This is an expanded version of a series of four lectures designed to show algebraists how ring theoretical methods can be used to analyze an interesting family of finite Markov chains. The chains happen to be random walks on semigroups, and the analysis is based on a study of the associated semigrou ..."
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This is an expanded version of a series of four lectures designed to show algebraists how ring theoretical methods can be used to analyze an interesting family of finite Markov chains. The chains happen to be random walks on semigroups, and the analysis is based on a study of the associated semigroup algebras. The paper
Locality Of Ds And Associated Varieties
, 1995
"... We prove that the pseudovariety DS, of all finite monoids each of whose regular Dclasses is a subsemigroup, is local. (A pseudovariety (or variety) V is local if any category whose local monoids belong to V divides a member of V). The proof uses the "kernel theorem" of the first two au ..."
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Cited by 14 (4 self)
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We prove that the pseudovariety DS, of all finite monoids each of whose regular Dclasses is a subsemigroup, is local. (A pseudovariety (or variety) V is local if any category whose local monoids belong to V divides a member of V). The proof uses the "kernel theorem" of the first two authors together with the description by P. Weil of DS as an iterated "block product". The onesided analogues of these methods provide wide new classes of local pseudovarieties of completely regular monoids. We conclude, however, with the third author's example of a variety (and a pseudovariety) of completely regular monoids that is not local. A pseudovariety V of monoids is said to be local if every finite category C whose local (or "loop") monoids belong to V divides a monoid in V. Locality has important applications to both the theory of pseudovarieties and to its connection with varieties of formal languages [20, 10]. The first author showed in [4] and with M. B. Szendrei in [7] that many pse...
On the Hyperdecidability of Semidirect Products of Pseudovarieties
 J. Pure and Applied Algebra
, 1997
"... The notion of hyperdecidability has been introduced as a tool which is particularly suited for granting decidability of semidirect products. It is shown in this paper that the semidirect product of an hyperdecidable pseudovariety with a pseudovariety whose finitely generated free objects are finite ..."
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Cited by 13 (9 self)
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The notion of hyperdecidability has been introduced as a tool which is particularly suited for granting decidability of semidirect products. It is shown in this paper that the semidirect product of an hyperdecidable pseudovariety with a pseudovariety whose finitely generated free objects are finite and effectively computable is again hyperdecidable. As instances of this result, one obtains, for example, the hyperdecidability of the pseudovarieties of all finite completely simple semigroups and of all finite bands of left groups. 1. Introduction The semidirect product is one of the most studied algebraic constructions in semigroup theory. In the theory of finite semigroups, applications such as the KrohnRhodes complexity have led to the study of the semidirect product as an operation on pseudovarieties and prompted the consideration of the decidability (of the membership) problem for pseudovarieties constructed as semidirect products. Although no example has yet been published, it is ...
The Lattice of Pseudovarieties of Idempotent Semigroups and a NonRegular Analogue
"... : We use classical results on the lattice L(B) of varieties of band (idempotent) semigroups to obtain information on the structure of the lattice P s(DA) of subpseudovarieties of DA,  where DA is the largest pseudovariety of finite semigroups in which all regular semigroups are band semigroups. ..."
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: We use classical results on the lattice L(B) of varieties of band (idempotent) semigroups to obtain information on the structure of the lattice P s(DA) of subpseudovarieties of DA,  where DA is the largest pseudovariety of finite semigroups in which all regular semigroups are band semigroups. We bring forward a lattice congruence on P s(DA), whose quotient is isomorphic to L(B), and whose classes are intervals with effectively computable least and greatest members. Also we characterize the proidentities satisfied by the members of an important family of subpseudovarieties of DA. Finally, letting V k be the pseudovariety generated by the kgenerated elements of DA (k 1), we use all our results to compute the position of the congruence class of V k in L(B). Introduction The lattice of pseudovarieties of finite semigroups has been the object of much attention over the past few decades, with motivations drawn not only from universal algebra, but also from theoretical computer scie...
Some Algorithmic Problems for Pseudovarieties
 Publ. Math. Debrecen
, 1996
"... Several algorithmic problems for pseudovarieties and their relationships are studied. This includes the usual membership problem and the computability of pointlike subsets of finite semigroups. Some of these problems afford equivalent formulations involving topological separation properties in fr ..."
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Cited by 6 (5 self)
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Several algorithmic problems for pseudovarieties and their relationships are studied. This includes the usual membership problem and the computability of pointlike subsets of finite semigroups. Some of these problems afford equivalent formulations involving topological separation properties in free profinite semigroups. Several examples are considered and, as an application, a decidability result for joins is proved. 1. Introduction Perhaps the three most celebrated results relating the theories of formal languages and finite semigroups are: Schutzenberger's characterization of starfree languages as those whose syntactic semigroups are finite and aperiodic [19]; Simon's characterization of piecewise testable languages as those whose syntactic semigroups are finite and Jtrivial [20]; and Brzozowski and Simon / McNaughton 's characterization of locally testable languages as those whose syntactic semigroups are finite local semilattices [7, 15]. These results led Eilenberg [9] to ...
The origins of combinatorics on words
, 2007
"... We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. These considerations gave rise to early results such as those of Axel Thue at the beginning of the 20th century. Other early ..."
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We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. These considerations gave rise to early results such as those of Axel Thue at the beginning of the 20th century. Other early results were obtained as a byproduct of investigations on various combinatorial objects. For example, paths in graphs are encoded by words in a natural way, and conversely, the Cayley graph of a group or a semigroup encodes words by paths. We give in this text an account of this twosided interaction.
Rational languages and the Burnside problem
 Theoret. Comput. Sci
, 1985
"... Abstract. The problem of finding regularity conditions for languages is, via the syntactic monoid, closely related to the classical Burnside problem. This survey paper presents several results and conjectures in this direction as well as on related subjects, including bounded languages, pumping, squ ..."
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Abstract. The problem of finding regularity conditions for languages is, via the syntactic monoid, closely related to the classical Burnside problem. This survey paper presents several results and conjectures in this direction as well as on related subjects, including bounded languages, pumping, squarefree words, commutativity, and rational power series. 1.
Maximal Groups in Free Burnside Semigroups
, 1998
"... . We prove that any maximal group in the free Burnside semigroup defined by the equation x n = x n+m for any n 1 and any m 1 is a free Burnside group satisfying x m = 1. We show that such group is free over a well described set of generators whose cardinality is the cyclomatic number of a gr ..."
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. We prove that any maximal group in the free Burnside semigroup defined by the equation x n = x n+m for any n 1 and any m 1 is a free Burnside group satisfying x m = 1. We show that such group is free over a well described set of generators whose cardinality is the cyclomatic number of a graph associated to the J class containing the group. For n = 2 and for every m 2 we present examples with 2m \Gamma 1 generators. Hence, in these cases, we have infinite maximal groups for large enough m. This allows us to prove important properties of Burnside semigroups for the case n = 2, which was almost completely unknown until now. Surprisingly, the case n = 2 presents simultaneously the complexities of the cases n = 1 and n 3: the maximal groups are cyclic of order m for n 3 but they can have more generators and be infinite for n 2; there are exactly 2 jAj J classes and they are easily characterized for n = 1 but there are infinitely many J classes and they are difficult to c...
Complexity Issues of the Pattern Equations in Idempotent Semigroups
, 1999
"... A pattern equation is a word equation of the form X = A where X is a sequence of variables and A is a sequence of constants. The problem whether X = A has a solution in a free idempotent semigroup (free band) is shown to be NPcomplete. ..."
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A pattern equation is a word equation of the form X = A where X is a sequence of variables and A is a sequence of constants. The problem whether X = A has a solution in a free idempotent semigroup (free band) is shown to be NPcomplete.