Parikhʼs theorem: A simple and direct automaton construction

Parikhʼs 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.

► We present a very simple automaton construction.
► Our construction takes a context-free grammar and returns a finite automaton.
► Input and output languages have the same Parikh image.