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Nondeterministic descriptional complexity of regular languages. (English) Zbl 1101.68657

Summary: We investigate the descriptional complexity of operations on finite and infinite regular languages over unary and arbitrary alphabets. The languages are represented by nondeterministic finite automata. In particular, we consider Boolean operations, catenation operations – concatenation, iteration, \(\lambda\)-free iteration – and the reversal. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. Otherwise tight bounds in the order of magnitude are shown.

MSC:

68Q45 Formal languages and automata
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[1] DOI: 10.1016/0304-3975(93)90160-U · Zbl 0786.68071
[2] DOI: 10.1007/BF01371727 · Zbl 0779.68061
[3] DOI: 10.1016/S0304-3975(00)00292-9 · Zbl 0984.68099
[4] DOI: 10.1016/0304-3975(86)90142-8 · Zbl 0638.68096
[5] Hopcroft J. E., Introduction to Automata Theory, Language, and Computation (1979) · Zbl 0426.68001
[6] DOI: 10.1016/S0022-0000(76)80038-4 · Zbl 0334.68044
[7] DOI: 10.1137/0222067 · Zbl 0799.68079
[8] Landau E., Archiv der Math., und Phys. 3 pp 92–
[9] Landau E., Handbuch der Lehre von der Verteilung der Primzahlen (1909) · JFM 40.0232.08
[10] DOI: 10.1016/S0304-3975(81)80005-9 · Zbl 0458.68017
[11] Mereghetti C., J. Aut. Lang., and Comb. 5 pp 287–
[12] DOI: 10.1137/S009753979935431X · Zbl 0980.68048
[13] DOI: 10.1142/S012905410200100X · Zbl 1066.68072
[14] Salomaa K., J. Aut., Lang., and Comb. 2 pp 177–
[15] DOI: 10.1016/0022-0000(80)90034-3 · Zbl 0445.68064
[16] Szalay M., Acta Arithm. 37 pp 321–
[17] DOI: 10.1007/978-3-642-59136-5_2
[18] Yu S., J. Aut. Lang. and Comb. 6 pp 221–
[19] Yu S., Bull. EATCS 76 pp 142–
[20] DOI: 10.1016/0304-3975(92)00011-F · Zbl 0795.68112
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