Abstract
This chapter discusses the regular expressions. Every regular set can be represented by a regular expression and every regular expression represents a regular set. Algebraic manipulations with regular expressions, and transition graphs are discussed. Various theorems are proved in the chapter. The chapter reviews sets of words corresponding to transition graphs, and presents the proof of Kleene's theorem. A procedure for checking equality of regular expressions, and an axiomatic approach to regular expressions is reviewed. Applying the standard logical rules of inference, for example, substitutivity of equality, and sometimes also special additional rules, which become in some sense a part of the system of axioms, one derives theorems from the axioms. One also looks for a concrete model of a mathematical structure satisfying a given set of axioms. The non-sufficiency of a finite system of axioms is also discussed in the chapter.
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