Some Properties of Brzozowski Derivatives of Regular Expressions
N.Murugesan, O.V.Shanmuga Sundaram
TL;DR
This paper explores properties of Brzozowski derivatives of regular expressions, providing lemmas, illustrating regular languages of derivatives, and proving generalizations as theorems to aid automaton construction.
Contribution
It introduces new lemmas and theorems on Brzozowski derivatives, enhancing understanding of their properties and applications in automata theory.
Findings
Regular languages of derivatives are characterized.
Lemmas of regular expressions are established.
Generalizations of derivatives are proved as theorems.
Abstract
Brzozowski derivatives of a regular expression are developed for constructing deterministic automata from the given regular expression in the algebraic way. In this paper,some lemmas of the regular expressions are discussed and the regular languages of the derivatives are illustrated. Also the generalizations of the Brzozowski derivatives are proved as theorems with help of properties and known results.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Logic, programming, and type systems