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A complete axiom system for algebra of closed-regular expression

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Automata, Languages and Programming (ICALP 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 172))

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Abstract

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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References

  1. Boasson, L. and Nivat, M., "Adherences of languages", JCSS, vol. 20, pp.285–309 (1980)

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  2. Izumi, H., Inagaki, Y. and Honda, N., "Right Linear Equations on Set Containing Infinite Sequences", The Transactions of the Institute of Electronics and Communication Engineers of Japan, Section D, vol. J66-D, no. 8, pp.993–999 (Aug., 1983)

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  3. Salomaa, A., "Two complete axiom systems for the algebra of regular events", JACM, vol. 13, pp.138–169, (1966)

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  4. Park, D., "Concurrency and automata on infinite sequences", Lecture Notes in Computer Sciences, no. 104, pp.167–183, Springer-Verlag (1981)

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  5. Izumi, H., Inagaki, Y., and Honda, N., "An algebra of Closed Regular Expression and A Complete Axiom System", Report of Technical Group, TGAL83-1, IECE, Japan (March, 1983)

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  6. Wagner, K., "Eine Axiomatisierung der Theorie der regularen Folgenmengen", EIK 12, 7, pp.337–354 (1976)

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Author notes

  1. Hiroyuki Izumi

    Present address: Presently, belonging to Fujitsu Laboratory, 211, Kawasaki, JAPAN

Authors and Affiliations

  1. Faculty of Engineering, Nagoya University, Furo-cho; Chikusa-ku, 464, Nagoya, JAPAN

    Hiroyuki Izumi & Yasuyoshi Inagaki

  2. Faculty of Engineering, Toyohashi University of Technology, Toyohashi, 440, Aichi Prefecture, JAPAN

    Namio Honda

Authors
  1. Hiroyuki Izumi
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  2. Yasuyoshi Inagaki
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  3. Namio Honda
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Jan Paredaens

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© 1984 Springer-Verlag Berlin Heidelberg

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Izumi, H., Inagaki, Y., Honda, N. (1984). A complete axiom system for algebra of closed-regular expression. In: Paredaens, J. (eds) Automata, Languages and Programming. ICALP 1984. Lecture Notes in Computer Science, vol 172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13345-3_23

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  • DOI: https://doi.org/10.1007/3-540-13345-3_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13345-2

  • Online ISBN: 978-3-540-38886-9

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