Abstract
A cover-automaton A of a finite language L ⊆ Σ* is a finite automaton that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic cover automaton of a finite language L usually has a smaller size than a minimal DFA that accept L. Thus, cover automata can be used to reduce the size of the representations of finite languages in practice. In this paper, we describe an efficient algorithm that, for a given DFA accepting a finite language, constructs a minimal deterministic finite coverautomaton of the language. We also give algorithms for the boolean operations on deterministic cover automata, i.e., on the finite languages they represent.
This research is supported by the Natural Sciences and Engineering Research Council of Canada grants OGP0041630.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.L. Balcàzar, J. Diaz, and J. Gabarrò, Uniform characterisations of non-uniform complexity measures, Information and Control 67 (1985) 53–89.
Y. Breitbart, On automaton and “zone” complexity of the predicate “tobe a kth power of an integer”,Dokl. Akad. Nauk SSSR 196 (1971), 16–19[Russian]; Engl. transl.,Soviet Math. Dokl. 12 (1971), 10-14.
Cezar C ampeanu. Regular languages and programming languages, Revue Roumaine de Linguistique-CLTA, 23 (1986), 7–10.
C. Dwork and L. Stockmeyer, A time complexity gap for two-way probabilistic finite-state automata, SIAM Journal on Computing 19 (1990) 1011–1023.
J. Hartmanis, H. Shank, Two memory bounds for the recognition of primes by automata, Math. Systems Theory 3 (1969), 125–129.
J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison Wesley (1979), Reading, Mass.
J. Kaneps, R. Freivalds, Minimal Nontrivial Space Space Complexity of Probabilistic One-Way Turing Machines, in Proceedings of Mathematical Foundations of Computer Science, Banská Bystryca, Czechoslovakia, August 1990, Lecture Notes in Computer Science, vol 452, pp. 355–361, Springer-Verlag, New York/Berlin, 1990.
J. Kaneps, R. Freivalds, Running time to recognise non-regular languages by 2-way probabilistic automata, in ICALP’91, Lecture Notes in Computer Science, vol 510, pp. 174–185, Springer-Verlag, New York/Berlin, 1991.
J. Paredaens, R. Vyncke, A class of measures on formal languages,Acta Informatica, 9 (1977), 73–86.
Jeffrey Shallit, Yuri Breitbart, Automaticity I: Properties of a Measure of Descriptional Complexity, Journal of Computer and System Sciences, 53, 10–25 (1996).
A. Salomaa, Theory of Automata, Pergamon Press (1969), Oxford.
K. Salomaa, S. Yu, Q. Zhuang, The state complexities of some basic operations on regular languages, Theoretical Computer Science 125 (1994) 315–328.
B.A. Trakhtenbrot, Ya. M. Barzdin, Finite Automata: Behaviour and Synthesis, Fundamental Studies in Computer Science, Vol.1, North-Holland, Amsterdam, 1973.
S. Yu, Q. Zhung, On the State Complexity of Intersection of Regular Languages, ACM SIGACT News, vol. 22,no. 3, (1991) 52–54.
S. Yu, Regular Languages, Handbook of Formal Languages, Springer Verlag, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Câmpeanu, C., Sântean, N., Yu, S. (1999). Minimal Cover-Automata for Finite Languages. In: Champarnaud, JM., Ziadi, D., Maurel, D. (eds) Automata Implementation. WIA 1998. Lecture Notes in Computer Science, vol 1660. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48057-9_4
Download citation
DOI: https://doi.org/10.1007/3-540-48057-9_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66652-3
Online ISBN: 978-3-540-48057-0
eBook Packages: Springer Book Archive