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Classification of finite monoids: the language approach. (English) Zbl 0471.20055


MSC:

20M35 Semigroups in automata theory, linguistics, etc.
68Q70 Algebraic theory of languages and automata
68Q45 Formal languages and automata
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References:

[1] Brzozowski, J. A.; Fich, F. E., Languages of \(R\)-trivial monoids, J. Comput. System Sci., 20, 32-49 (1980) · Zbl 0446.68066
[2] Eilenberg, S., Automata, Languages, and Machines, Vol. B (1976), Academic Press: Academic Press New York · Zbl 0359.94067
[3] Hall, M., The Theory of Groups (1976), Chelsea: Chelsea New York · Zbl 0354.20001
[4] Lallement, G., Semigroups and Combinatorial Applications (1979), Wiley: Wiley New York · Zbl 0421.20025
[5] Myhill, J., Finite automata and the representation of events, (WADD Technical Report 57-624 (1957), Wright-Patterson Air Force Base) · Zbl 0122.01102
[6] Schützenberger, M. P., On finite monoids having only trivial subgroups, Information and Control, 8, 190-194 (1965) · Zbl 0131.02001
[7] Simon, I., Piecewise testable events, (Brakhage, H., Automata Theory and Formal Languages. Automata Theory and Formal Languages, Lecture Notes in Computer Science, 33 (1975), Springer: Springer Berlin), 214-222 · Zbl 0316.68034
[8] Straubing, H., Families of recognizable sets corresponding to certain varieties of finite monoids, J. Pure Appl. Algebra, 15, 305-318 (1979) · Zbl 0414.20056
[9] Straubing, H., A generalization of the Schützenberger product of finite monoids, Theoret. Comput. Sci., 13, 137-150 (1981) · Zbl 0456.20048
[10] Thérien, D., Classification of regular languages with congruences, (Ph.D. Thesis (1980), Department of Computer Science, University of Waterloo: Department of Computer Science, University of Waterloo Waterloo, Ontario, Canada), Research Report CS-80-19
[11] Thérien, D., Languages of nilpotent and solvable groups, (Maurer, H. A., Automata Languages and Programming, 71 (1979), Springer: Springer Berlin), 616-632, Lecture Notes in Computer Science · Zbl 0416.20058
[12] B. Tilson, Chapter XI and XII in [2].; B. Tilson, Chapter XI and XII in [2].
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