Partial Derivatives for Context-Free Languages: From $\mu$-Regular Expressions to Pushdown Automata

TL;DR

This paper extends the concept of partial derivatives from regular expressions to $$-regular expressions for context-free languages, enabling a new automaton construction.

Contribution

It introduces a novel extension of partial derivatives to $$-regular expressions and proves their correctness and finiteness, leading to a generalized pushdown automaton construction.

Findings

Proves correctness of extended partial derivatives.

Shows finiteness of iterated partial derivatives.

Constructs a nondeterministic pushdown automaton from $$-regular expressions.

Abstract

We extend Antimirov's partial derivatives from regular expressions to $\mu$-regular expressions that describe context-free languages. We prove the correctness of partial derivatives as well as the finiteness of the set of iterated partial derivatives. The latter are used as pushdown symbols in our construction of a nondeterministic pushdown automaton, which generalizes Antimirov's NFA construction.