Derivatives of Regular Expressions

Kleene's regular expressions, which can be used for describing sequential circuits, were defined using three operators (union, concatenation and iterate) on sets of sequences.Word descriptions of problems can be more easily put in the regular expression language if the language is enriched by the inclusion of other logical operations.However, il~ the problem of converting the regular expression description to a state diagram, the existing methods either cannot handle expressions with additional operators, or are made quite complicated by the presence of such operators.In this paper the notion of a derivative of a regular expression is introduced atld the properties of derivatives are discussed.This leads, in a very natural way, to the construction of a state diagram from a regular expression containing any number of logical operators.