A complete axiom system for algebra of closed-regular expression

  • Hiroyuki Izumi
  • Yasuyoshi Inagaki
  • Namio Honda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 172)


In this paper we have introduced the concept of cl-regular expression, proposed the axiom system & for cl-regular expressions, and proved the soundness and completeness of the system &. The system & will be a base for algebraic studies on cl-regular sets. On the other hand, the system & coincides with the Salomm's axiom system if we restrict the objects to the regular sets of finite strings. In this sense, our axiom system is a natural extension of Salomaa's axiom system to allow cl-regular set including infinite strings.

The referee kindly informed the authors that an axiom system for ω-regular expressions has earlier been introduced by K. Wagner [6]. But the use of closed regular expressions in this paper leads to our axiom system &, a more elegant and natural one than the use of ω-regular expressions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Hiroyuki Izumi
    • 1
  • Yasuyoshi Inagaki
    • 1
  • Namio Honda
    • 2
  1. 1.Faculty of EngineeringNagoya UniversityNagoyaJAPAN
  2. 2.Faculty of EngineeringToyohashi University of TechnologyAichi PrefectureJAPAN

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