No CrossRef data available.
Article contents
Strongly locally testable semigroupswith commuting idempotentsand related languages
Published online by Cambridge University Press: 15 August 2002
Abstract
If we consider words over the alphabet which is the set of all elementsof a semigroup S, then such a word determines an element of S:the product of the letters of the word. S is strongly locally testable if whenever two words over thealphabet S have the same factors of a fixed length k, then the products of the letters of these words are equal. We had previously proved [19] thatthe syntactic semigroup of a rational language L is strongly locally testable if and only ifL is both locally and piecewise testable. We characterize in this paper the variety of strongly locally testable semigroups with commuting idempotents and, using the theory of implicit operations on avariety of semigroups, we derive an elementary combinatorial description of the related variety of languages.
Information
- Type
- Research Article
- Information
- Copyright
- © EDP Sciences, 1999
References
J. Almeida, Finite Semigroups and Universal Algebra, River Edge. N.J. World Scientific, Singapore (1994).
J. Almeida, Equations for pseudovarieties, J.-E. Pin Ed., Formal properties of finite automata and applications, Springer, Lecture Notes in Computer Science
386 (1989).
Almeida, J., Implicit operations on finite J-trivial semigroups and a conjecture of I. Simon.
J. Pure Appl. Algebra
69 (1990) 205-218.
CrossRef
Almeida, J., On pseudovarieties, varietes of languages, filters of congruences, pseudoidentities and related topics.
Algebra Universalis
27 (1990) 333-350.
CrossRef
J. Almeida and P. Weil, Relatively free profinite monoids: an introduction and examples, J.B. Fountain and V.A.R. Gould Eds., Semigroups, Formal Languages and Groups (to appear) (Da rivedere).
J. Almeida and P. Weil, Free profinite semigroups over semidirect products, Izv. VUZ Matematika 39 (1995) 3-31; English version, Russian Mathem. (Izv. VUZ.) 39 (1995) 1-28.
Ash, C.J., Hall, T.E. and Pin, J.-E., On the varieties of languages associated with some varieties of finite monoids with commuting idempotents.
Inform. and Computation
86 (1990) 32-42.
CrossRef
Beauquier, D. and Pin, J.-E., Languages and scanners.
Theoret. Comput. Sci.
84 (1991) 3-21.
CrossRef
Brzozowski, J.A. and Simon, I., Characterization of locally testable events.
Discrete Math.
4 (1973) 243-271.
CrossRef
S. Eilenberg, Automata, languages and machines. Academic Press, New York, Vol. B (1976).
Eilenberg, S. and Schützenberger, M.P., On pseudovarieties.
Adv. in Math.
19 (1976) 413-418.
CrossRef
McNaughton, R., Algebraic decision procedures for local testability.
Math. Systems Theory
8 (1974) 60-76.
CrossRef
J.-E. Pin, Variétés de Langages Formels, Masson, Paris (1984).
J.-E. Pin and H. Straubing, Monoids of upper triangular matrices. Colloq. Math. Societatis Janos Bolyai 39 Semigroups, Szeged (1981) 259-272.
Reiterman, J., The Birkhoff theorem for finite algebras.
Algebra Universalis
14 (1982) 1-10.
CrossRef
Schützenberger, M.P., On finite monoids having only trivial subgroups.
Inform. and Control
8 (1965) 190-194.
CrossRef
C. Selmi, Langages et semigroupes testables. Doctoral thesis, University of Paris VII, Paris (1994).
Simon, I., Piecewise testable events. Proc. 2nd GI Conf., Springer,
Lecture Notes in Computer Science
33 (1975) 214-222.
CrossRef
P. Weil, Implicit operations on pseudovarieties: an introduction, J. Rhodes Ed., World Scientific, Singapore, Semigroups and Monoids and Applications (1991).
Zalcstein, Y., Locally testable languages.
J. Computer and System Sciences
6 (1972) 151-167.
CrossRef
M. Zeitoun, Opérations implicites et variétés de semigroupes finis. Doctoral thesis, University of Paris VII, Paris (1993).