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