A fully equational proof of Parikh's theorem

Aceto, Luca; Ésik, Zoltán; Ingólfsdóttir, Anna

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 2, pp. 129-153.

We show that the validity of Parikh’s theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of $\mu$-term equations of continuous commutative idempotent semirings.

Classification : 03C05, 16Y60, 68Q70
Mots clés : Parikh's theorem, commutative context-free languages, commutative rational languages, equational logic, varieties, complete axiomatizations, commutative idempotent semirings, algebraically complete commutative idempotent semirings

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