Abstract
This chapter presents the algebra of regular expressions. The star operator (*) is fundamental in the theory of finite deterministic automata. to the chapter presents a formal characterization of the set of valid equations between regular expressions. The star height of a regular language L, in symbols sh(L), is the least integer i such that, for some regular expression a, L = |a| and the star height of α equals i. As any finite language that does not contain the empty word has star height 0 and the construction of the sequence of languages L1 is possible whenever the alphabet contains at least two letters. The n-dimensional row vectors Y and n × n matrices Z whose elements are languages are also elaborated in the chapter.
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