Duality and equational theory of regular languages

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5126 LNCS, Issue PART 2, 2008, Pages 246-257

  Gehrke, Mai ^a   Grigorieff, Serge ^b   Pin, Jean Éric ^b  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

^b UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49149118541     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-70583-3_21     Document Type: Conference Paper

References (23)

1. Adams, M.E.: The Frattini sublattice of a distributive lattice. Alg. Univ. 3, 216-228 (1973)
2. Almeida, J.: Residually finite congruences and quasi-regular subsets in uniform algebras. Partugaliæ Mathematica 46, 313-328 (1989)
3. Almeida, J.: Finite semigroups and universal algebra. World Scientific Publishing Co. Inc., River Edge (1994)
4. Almeida, J.: Profinite semigroups and applications. In: Structural theory of automata, semigroups, and universal algebra. NATO Sci. Ser. II Math. Phys. Chem., vol. 207, pp. 1-45. Springer, Dordrecht (2005); Notes taken by Alfredo Costa
5. Almeida, J., Volkov, M.V.: Profinite identities for finite semigroups whose subgroups belong to a given pseudovariety. J. Algebra Appl. 2(2), 137-163 (2003)
6. Birkhoff, G.: On the structure of abstract algebras. Proc. Cambridge Phil. Soc. 31, 433-454 (1935)
7. Eilenberg, S.: Automata, languages, and machines, vol. B. Academic Press [Harcourt Brace Jovanovich Publishers], New York (1976)
8. Ésik, Z.: Extended temporal logic on finite words and wreath products of monoids with distinguished generators. In: Ito, M., Toyama, M. (eds.) DLT 2002. LNCS, vol. 2450, pp. 43-58. Springer, Heidelberg (2003)
9. Goldblatt, R.: Varieties of complex algebras. Ann. Pure App. Logic 44, 173-242 (1989)
10. Kunc, M.: Equational description of pseudovarieties of homomorphisms. Theoretical Informatics and Applications 37, 243-254 (2003)
11. Pin, J.-E.: A variety theorem without complementation. Russian Mathematics (Iz. VUZ) 39, 80-90 (1995)
12. Pin, J.-É., Straubing, H.: Some results on script C-varieties. Theoret. Informatics Appl. 39, 239-262 (2005)
13. Pin, J.-É., Weil, P.: A Reiterman theorem for pseudovarieties of finite first-order structures. Algebra Universalis 35, 577-595 (1996)
14. Pippenger, N.: Regular languages and Stone duality. Theory Comput. Syst. 30(2), 121-134 (1997)
15. Polák, L.: Syntactic semiring of a language. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 611-620. Springer, Heidelberg (2001)
16. Priestley, H.A.: Representation of distributive lattices by means of ordered Stone spaces. Bull. London Math. Soc. 2, 186-190 (1970)
17. Reilly, N.R., Zhang, S.: Decomposition of the lattice of pseudovarieties of finite semigroups induced by bands. Algebra Universalis 44(3-4), 217-239 (2000)
18. Reiterman, J.: The Birkhoff theorem for finite algebras. Algebra Universalis 14(1), 1-10 (1982)
19. Stone, M.: The theory of representations for Boolean algebras. Trans. Amer. Math. Soc. 40, 37-111 (1936)
20. Stone, M.H.: Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc. 41(3), 375-481 (1937)
21. Straubing, H.: On logical descriptions of regular languages. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 528-538. Springer, Heidelberg (2002)
22. Weil, P.: Profinite methods in semigroup theory. Int. J. Alg. Comput. 12, 137-178 (2002)
23. Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of language theory, ch. 2, vol. 1, pp. 679-746. Springer, Heidelberg (1997)