Parikh's Theorem: A simple and direct automaton construction
Javier Esparza, Pierre Ganty, Stefan Kiefer, Michael Luttenberger
TL;DR
This paper introduces a straightforward automaton construction that, given a context-free grammar, efficiently produces a finite automaton recognizing a regular language with the same Parikh image, simplifying analysis of context-free languages.
Contribution
It provides a simple and direct method to construct automata that match the Parikh image of context-free languages, improving understanding and tools for language analysis.
Findings
Automaton construction is simple and efficient.
The automaton recognizes a regular language with the same Parikh image.
The method simplifies analysis of context-free languages.
Abstract
Parikh's theorem states that the Parikh image of a context-free language is semilinear or, equivalently, that every context-free language has the same Parikh image as some regular language. We present a very simple construction that, given a context-free grammar, produces a finite automaton recognizing such a regular language.
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