Abstract
We characterize the varieties of rational languages closed under products with counter. They are exactly the varieties that correspond via Eilenberg's theorem to the varieties of monoids closed under inverse LG sol -relational morphisms. This yields some decidability results for certain classes of rational languages.
This work was supported by the P.R.C. Mathématique et Informatique.
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References
A. Azevedo. Operações implícitas sobre pseudovariedades de semigrupos, aplicações, Doctoral Dissertation, Universidade do Porto, Porto, 1989.
D. Barrington. Bounded-width polynomial-size branching programs recognize only those languages in NC 1, in Proc. 18th A.C.M. S.T.O.C., 1986, pp. 1–5.
S. Eilenberg. Automata, Languages and Machines, vol. B, Academic Press (New York), 1976.
S. Kleene. Representation of events in nerve nets and finite automata, in Automata Studies (Shannon and McCarthy eds.), Princeton University Press, (Princeton) 1954, pp. 3–51.
J.-E. Pin. Concatenation hierarchies and decidability results, in Combinatorics on Words, Progress and Perspectives (L. Cummings ed.), Academic Press, 1983, pp. 195–228.
J.-E. Pin. Varitétés de langages formels, Masson (Paris), 1984, and Varieties of formal languages, North Oxford Academic (London), 1986 and Plenum (New-York), 1986.
J.-E. Pin. Topologies for the free monoid, to appear in Journal of Algebra.
J. Rhodes and B. Tilson. The kernel of monoid morphisms: a reversal-invariant decomposition theory, preprint.
J. Rhodes and P. Weil. Decomposition techniques for finite semigroups, part 1, to appear in Journal of Pure and Applied Algebra.
J. Rhodes and P. Weil. Decomposition techniques for finite semigroups, part 2, to appear in Journal of Pure and Applied Algebra.
M.-P. Schützenberger. On finite monoids having only trivial subgroups, in Information and Control 8 (1965), pp. 190–194.
M.-P. Schützenberger. Sur le produit de concaténation non ambigu, in Semigroup Forum 13 (1976), pp. 47–75.
I. Simon. Piecewise testable events, in Proc. 2nd G.I. Conf., Lecture Notes in Computer Science 33, Springer (1975), pp.214–222.
H. Straubing. Recognizable sets and power sets of finite semigroups, in Semigroup Forum 18 (1979), pp. 331–340.
H. Straubing. Families of recognizable sets corresponding to certain varieties of finite monoids, in Journal of Pure and Applied Algebra 15 (1979), pp. 305–318.
H. Straubing. Aperiodic homomorphisms and the concatenation product of recognizable sets, in Journal of Pure and Applied Algebra 15 (1979), pp. 319–327.
H. Straubing. A generalization of the Schützenberger product of finite monoids, in Theoretical Computer Science 13 (1981), pp. 137–150.
H. Straubing. Semigroups and languages of dot-depth two, in Theoretical Computer Science 58 (1988), pp. 361–378.
H. Straubing, D. Thérien and W. Thomas. Regular languages defined with generalized quantifiers, to appear.
D. Thérien. Languages of nilpotent and solvable groups, in Proc. 6th I.C.A.L.P., Lecture Notes in Computer Science 71, Springer, Berlin (1979), pp. 616–632.
D. Thérien. Classification of finite monoids: the language approach, in Theoretical Computer Science 14 (1981), pp. 195–208.
D. Thérien. Subword counting and nilpotent groups, in Combinatorics on Words, Progress and Perspectives (L. Cummings ed.), Academic Press, 1983, pp. 297–305.
B. Tilson. Chapters XI and XII in [3].
P. Weil. Produits et décomposition d'automates, applications à la théorie des langages, thèse de troisième cycle, Université de Paris 7 (1985).
P. Weil. Inverse monoids and the dot-depth hierarchy, Ph.D. Thesis, University of Nebraska, Lincoln, 1988.
P. Weil. Concatenation product: a survey, to appear in Actes de l'Ecole de Printemps d'Inform. Th., Ramatuelle, 1988.
P. Weil. An extension of the Schützenberger product, to appear.
P. Weil. Products of languages with counter, to appear in Theoretical Computer Science.
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Weil, P. (1989). On varieties of languages closed under products with counter. In: Kreczmar, A., Mirkowska, G. (eds) Mathematical Foundations of Computer Science 1989. MFCS 1989. Lecture Notes in Computer Science, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51486-4_99
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DOI: https://doi.org/10.1007/3-540-51486-4_99
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