Product Derivatives of Regular Expressions

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Abstract

We propose a novel extension of Brzozowski's derivative of regular expressions, called product derivatives. It takes two regular expressions and the meaning of its result is stated as follows: a product derivative of R with respect to S is a regular expression obtained by the consumption of all the sequences in the first regular expression by the second, i.e., the result is the product of Brzozowski's derivatives of R with respect to sequences in S. We develop an algorithm for our derivatives in coinductive manner. The termination of the algorithm is shown based on the proof method by Brandt and Henglein. We expect the derivative proposed in this talk is an important step to the development of the derivatives of a regular hedge expression taking a regular hedge expression as input, which is useful for transformation of XML documents with function terms typed with regular hedge expressions. The situation, for example, occurs in the transformation of XML documents with the links to the other Web services, such as Active XML documents.

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