Construction of a Deterministic ω-Automaton Using Derivatives

Roman R. Redziejowski

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 33, Issue: 2, page 133-158
  • ISSN: 0988-3754

Abstract

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A deterministic automaton recognizing a given ω-regular language is constructed from an ω-regular expression with the help of derivatives. The construction is related to Safra's algorithm, in about the same way as the classical derivative method is related to the subset construction.

How to cite

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Redziejowski, Roman R.. "Construction of a Deterministic ω-Automaton Using Derivatives." RAIRO - Theoretical Informatics and Applications 33.2 (2010): 133-158. <http://eudml.org/doc/222031>.

@article{Redziejowski2010,
abstract = { A deterministic automaton recognizing a given ω-regular language is constructed from an ω-regular expression with the help of derivatives. The construction is related to Safra's algorithm, in about the same way as the classical derivative method is related to the subset construction. },
author = {Redziejowski, Roman R.},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Infinite word; omega-language; regular language; regular expression; rational language; rational expression; derivative; deterministic omega-automaton; Muller automaton.; -regular language; Safra's algorithm},
language = {eng},
month = {3},
number = {2},
pages = {133-158},
publisher = {EDP Sciences},
title = {Construction of a Deterministic ω-Automaton Using Derivatives},
url = {http://eudml.org/doc/222031},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Redziejowski, Roman R.
TI - Construction of a Deterministic ω-Automaton Using Derivatives
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 2
SP - 133
EP - 158
AB - A deterministic automaton recognizing a given ω-regular language is constructed from an ω-regular expression with the help of derivatives. The construction is related to Safra's algorithm, in about the same way as the classical derivative method is related to the subset construction.
LA - eng
KW - Infinite word; omega-language; regular language; regular expression; rational language; rational expression; derivative; deterministic omega-automaton; Muller automaton.; -regular language; Safra's algorithm
UR - http://eudml.org/doc/222031
ER -

References

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  2. J.A. Brzozowski, Derivatives of regular expressions. J. Assoc. Comput. Mach.11 (1964) 481-494.  Zbl0225.94044
  3. J.A. Brzozowski and E. Leiss, On equations for regular languages, finite automata, and sequential networks. Theoret. Comput. Sci.10 (1980) 19-35.  Zbl0415.68023
  4. J.H. Conway, Regular Algebra and Finite Machines. Chapman and Hall (1971).  Zbl0231.94041
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  8. J.-E. Pin, Varieties of Formal Languages. North Oxford Academic (1986).  
  9. 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).  
  10. S. Safra, On the complexity of ω-automata, in Proc. 29th Annual Symposium on Foundations of Computer ScienceIEEE (1988) 319-327.  
  11. L. Staiger, Finite-state ω-languages. J. Comput. System Sci.27 (1983) 434-448.  Zbl0541.68052
  12. L. Staiger, The entropy of finite-state ω-languages. Problems of Control and Information Theory14 (1985) 383-392.  Zbl0582.94012
  13. L. Staiger, ω-languages. In Handbook of Formal Languages, G. Rozenberg and A. Salomaa, Eds., 3, Springer-Verlag (1997) 339-387.  
  14. W. Thomas, Automata on infinite objects, in Handbook of Theoretical Computer Science, J. van Leeuven, Ed., B, Elsevier Science Publishers (1990) 133-191.  

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