×
Yu, Sheng; Zhuang, Qingyu; Salomaa, Kai

The state complexities of some basic operations on regular languages. (English) Zbl 0795.68112

Theor. Comput. Sci. 125, No. 2, 315-328 (1994).
Summary: We consider the state complexities of some basic operations on regular languages. We show that the number of states that is sufficiently and necessary in the worst case for a deterministic finite automaton (DFA) to accept the catenation of an \(m\)-state DFA language and an \(n\)-state DFA language is exactly \(m2^ n- 2^{n-1}\), for \(m,n\geq 1\). The result of \(2^{n-1}+ 2^{n-2}\) states is obtained for the star of an \(n\)-state DFA language, \(n>1\). State complexities for other basic operations and for regular languages over a one-letter alphabet are also studied.

Cited in 126 Documents

MSC:

68Q45 Formal languages and automata
68Q25 Analysis of algorithms and problem complexity

Keywords:

state complexities; regular languages; deterministic finite automaton
PDF BibTeX XML Cite
\textit{S. Yu} et al., Theor. Comput. Sci. 125, No. 2, 315--328 (1994; Zbl 0795.68112)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Chandra, A. K.; Kozen, D. C.; Stockmeyer, L. J., Alternation, J. ACM, 28, 114-133 (1981) · Zbl 0473.68043
[2] Fellah, A.; Jürgensen, H.; Yu, S., Constructions for alternating finite automata, Internat. J. Comput. Math., 35, 117-132 (1990) · Zbl 0699.68081
[3] Hopcroft, J. E.; Ullman, J. D., Introduction to Automata Theory, Languages, and Computation (1979), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0196.01701
[4] Jiang, T.; Ravikumar, B., Minimal NFA problems are hard, (Proc. 18th ICALP. Proc. 18th ICALP, Lecture Notes in Computer Science, Vol. 510 (1991), Springer: Springer Berlin), 629-640 · Zbl 0766.68063
[5] Leiss, E., Succinct representation of regular languages by boolean automata, Theoret. Comput., 13, 323-330 (1981) · Zbl 0458.68017
[6] Meyer, A. R.; Fischer, M. J., Economy of description by automata, grammars, and formal systems, FOCS, 12, 188-191 (1971)
[7] Ravikumar, B., Some applications of a technique of Sakoda and Sipser, SIGACT News, 21, 4, 73-77 (1990)
[8] Ravikumar, B.; Ibarra, O. H., Relating the type of ambiguity of finite automata to the succinctness of their representation, SIAM J. Comput., 18, 6, 1263-1282 (1989) · Zbl 0692.68049
[9] Salomaa, A., Theory of Automata (1969), Pergamon: Pergamon Oxford · Zbl 0193.32901
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.