On algorithmic problems for joins of pseudovarieties

Semigroup Forum

Volumn 62, Issue 1, 2001, Pages 1-40

  Steinberg, Benjamin ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009886575     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00020979     Document Type: Article

References (28)

1. Albert, D., R. Baldinger, and J. Rhodes, Undecidability of the identity problem for finite semigroups, J. Symb. Logic 57 (1992) 179-192.
2. Almeida, J., "Finite Semigroups and Universal Algebra", World Scientific, Singapore, 1994.
3. Almeida, J., Hyperdecidable pseudovarieties and the calculation of semidirect products, Int. J. Alg. and Comp. 9 (1999) 241-261.
4. Almeida, J., A. Azevedo, and M. Zeitoun, Pseudovariety joins involving J-trivial semigroups, Int. J. Alg. and Comp. 9 (1999) 99-112.
5. Almeida, J., and P. V. Silva, On the hyperdecidability of semidirect products of pseudovarieties, Comm. in Algebra 26 (1998) 4065-4077.
6. Almeida, J., and B. Steinberg, On the decidability of iterated semidirect products with applications to complexity, Proc. London Math. Soc. 80 (2000) 50-74.
7. Almeida, J., and P. Weil, Reduced factorizations in free profinite groups and the join decompositions of pseudovarieties, Int. J. Alg. and Comp. 3 (1994) 375-403.
8. Almeida, J., Relatively free profinite monoids: an introduction and examples, "Semigroups, Formal Languages and Groups", ed. John Fountain, Kluwer Academic Publishers, Dordrecht, 1995, 73-117.
9. Almeida, J., and M. Zeitoun, The pseudovariety J is hyperdecidable, Theor. Inf. and Applications 31 (1997) 457-482.
10. Ash, C. J., Inevitable graphs: A proof of the type II conjecture and some related decision procedures, Int. J. Alg. and Comp. 1 (1991) 127-146.
11. Delgado, M., Abelian pointlikes of a monoid, Semigroup Forum 56 (1998) 339-361.
12. Delgado, M., On the hyperdecidability of pseudovarieties of groups, Int. J. Alg. and Comp., to appear.
13. Eilenberg, S., "Automata, Languages and Machines", Academic Press, New York, Vol A, 1974: Vol B, 1976.
14. Eilenberg, S., "Automata, Languages and Machines", Academic Press, New York, Vol A, 1974: Vol B, 1976
15. Henckell, K., Pointlike sets: The finest aperiodic cover of a finite semigroup, J. Pure Appl. Alg. 55 (1988) 85-126.
16. Henckell, K., S. W. Margolis, J. -E. Pin, and J. Rhodes, Ash's type II theorem, profinite topology and Malcev products, Int. J. Alg. and Comp. 1 (1991) 411-436.
17. MacLane, S., "Categories for the Working Mathematician", Springer-Verlag, New York, 1971.
18. Pin, J.-E., "Varieties of Formal Languages", Plenum, New York, 1986.
19. Pin, J.-E., and P. Weil, Profinite semigroups, Mal'cev products, and identities, J. Algebra 182 (1996) 604-626.
20. Reiterman, J., The Birkhoff theorem for finite algebras, Algebra Universalis 14 (1982) 1-10.
21. Rhodes, J., Undecidability, automata, and pseudovarieties of finite semigroups, Int. J. Alg. and Comp. 9 (1999) 455-473.
22. Rhodes, J., and B. Steinberg, Pointlike sets, hyperdecidability, and the identity problem for finite semigroups, Int. J. Alg. and Comp. 9 (1999) 475-481.
23. Simon, I., Piecewise testable events, Proc. 2nd Gl Conf, Lect. Notes in Comp. Sci. 33, Springer-Verlag, New York, 1975, 214-222.
24. Steinberg, B., Decidability and hyperdecidability of joins of pseudovarieties, Ph. D. Thesis, University of California at Berkeley, 1998.
25. Steinberg, B., On pointlike sets and joins of pseudovarieties, Int. J. Alg. and Comp. 8 (1998) 203-231.
26. Steinberg, B., Inevitable graphs and profinite topologies: Some solutions to algorithmic problems in monoid and automata theory stemming from group theory, Int. J. Alg. and Comp., to appear.
27. Steinberg, B., Monoid kernels and profinite topologies on the free Abelian group, Bull. Austral. Math. Soc. 60 (1999) 391-402.
28. Trotter, P. G., and M. V. Volkov, The finite basis problem in the pseudovariety joins of aperiodic semigroups with groups, Semigroup Forum 52 (1996) 83-91.