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
Boasson, L. and Nivat, M., "Adherences of languages", JCSS, vol. 20, pp.285–309 (1980)
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)
Salomaa, A., "Two complete axiom systems for the algebra of regular events", JACM, vol. 13, pp.138–169, (1966)
Park, D., "Concurrency and automata on infinite sequences", Lecture Notes in Computer Sciences, no. 104, pp.167–183, Springer-Verlag (1981)
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)
Wagner, K., "Eine Axiomatisierung der Theorie der regularen Folgenmengen", EIK 12, 7, pp.337–354 (1976)
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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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