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Construction of a Deterministic ω-Automaton Using Derivatives

Published online by Cambridge University Press:  15 August 2002

Roman R. Redziejowski
Roman R. Redziejowski*
Affiliation:
Ericsson Hewlett-Packard Telecommunications AB, Västberga Allé 9, S-12625 Stockholm, Sweden; roman.redziejowski@ehpt.com
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Abstract

A deterministic automaton recognizing a givenω-regular languageis constructed from an ω-regular expressionwith the help of derivatives.The construction is related to Safra's algorithm, in about the same way as the classicalderivative method is related to the subset construction.

Keywords

Infinite wordomega-languageregular languageregular expressionrational languagerational expressionderivativedeterministic omega-automatonMuller automaton.

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 2 , March 1999 , pp. 133 - 158
Copyright
© EDP Sciences, 1999

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References

V. Antimirov, Partial derivatives of regular expressions and finite automata constructions. In STACS 95, E.W. Mayr and C. Puech, Eds., Springer-Verlag (1995) 455-466.
Brzozowski, J.A., Derivatives of regular expressions. J. Assoc. Comput. Mach. 11 (1964) 481-494. CrossRef
Brzozowski, J.A. and Leiss, E., On equations for regular languages, finite automata, and sequential networks. Theoret. Comput. Sci. 10 (1980) 19-35. CrossRef
J.H. Conway, Regular Algebra and Finite Machines. Chapman and Hall (1971).
D. Park, Concurrency and automata on infinite sequences, in Proc. 5th GI Conference, Karlsruhe, Springer-Verlag, Lecture Notes in Computer Science 104 (1981) 167-183.
D. Perrin, Finite automata, in Handbook of Theoretical Computer Science, J. van Leeuven, Ed., B, Elsevier Science Publishers (1990) 1-57.
D. Perrin and J.-E. Pin, Mots infinis. Internal report LITP 93.40, Laboratoire Informatique Théorique et Programmation, Institut Blaise Pascal, 4 Place Jussieu, F-75252 Paris Cedex 05 (1993).
J.-E. Pin, Varieties of Formal Languages. North Oxford Academic (1986).
R.R. Redziejowski, The theory of general events and its application to parallel programming. Technical paper TP 18.220, IBM Nordic Laboratory, Lidingö, Sweden (1972).
S. Safra, On the complexity of ω-automata, in Proc. 29th Annual Symposium on Foundations of Computer Science IEEE (1988) 319-327.
Staiger, L., Finite-state ω-languages. J. Comput. System Sci. 27 (1983) 434-448. CrossRef
Staiger, L., The entropy of finite-state ω-languages. Problems of Control and Information Theory 14 (1985) 383-392.
L. Staiger, ω-languages. In Handbook of Formal Languages, G. Rozenberg and A. Salomaa, Eds., 3, Springer-Verlag (1997) 339-387.
W. Thomas, Automata on infinite objects, in Handbook of Theoretical Computer Science, J. van Leeuven, Ed., B, Elsevier Science Publishers (1990) 133-191.