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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