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Bounds on the index and period of a binary relation on a finite set. (English) Zbl 0353.20055


MSC:

20M20 Semigroups of transformations, relations, partitions, etc.
20M35 Semigroups in automata theory, linguistics, etc.
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References:

[1] Birkhoff, G., Lattice Theory, AMS Colloq. Publ. Vol XXV, Providence, RI, 1967. · Zbl 0153.02501
[2] Brandon, R. L.; Hardy, D. W.; Markowsky, G., The Schützenberger Group of an H-class in the Semigroup of Binary Relations, Semigroup Forum, 5, 45-53 (1972) · Zbl 0259.20056 · doi:10.1007/BF02572873
[3] Clifford, A.H. and G.B. Preston, The Algebraic Theory of Semigroups, AMS Surveys, Vol. I, Providence, RI, 1961. · Zbl 0111.03403
[4] Hopcroft, J. E.; Ullman, J. D., Formal Languages and Their Relation to Automata (1969), Reading, MA: Addison-Wesley, Reading, MA · Zbl 0196.01701
[5] Landau, E., Handbuch Verteilung der Primzahlen, 1, 222-229 (1909)
[6] Mandl, R., Precise Bounds Associated With the Subset Construction on Various Classes of Nondeterministic Finite Automata, Proc. 7th Annual Princeton Conf. on Info. Sciences and Systems, 1973, 263-267.
[7] Moore, F.R., On the Bounds for State-Set Size in the Proofs of Equivalence Between Deterministic, Nondeterministic, and Two-Way Automata, IEEE Trans. on Computers 20, 1211-1214 · Zbl 0229.94033
[8] Schein, B. M., Remarks on Research Problem T45, Semigroup Forum, Vol. 4, p. 373.
[9] Zaretskii, K. A., The Semigroup of Binary Relations, Mat. Sbornik, 61, 291-305 (1963) · Zbl 0125.28003
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