2002
DOI: 10.1051/ita:2002007
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A Fully Equational Proof of Parikh's Theorem

Abstract: 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 µ-term equations of continuous commutative idempotent semirings.

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Cited by 8 publications
(3 citation statements)
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“…In [2] Parikh's theorem is derived from a small set of purely equational axioms involving fixed points. It is hard to derive a construction from this proof.…”
Section: Conclusion and Related Workmentioning
confidence: 99%
“…In [2] Parikh's theorem is derived from a small set of purely equational axioms involving fixed points. It is hard to derive a construction from this proof.…”
Section: Conclusion and Related Workmentioning
confidence: 99%
“…It states that the Parikh image of any context-free language (CFL), that is, language accepted by a pushdown automaton (PDA), is a semilinear set (for a proof, see, e.g., [1,11]). Hence, CFLs are indistinguishable from regular languages unless the order of letters is concerned; as a corollary, over a unary alphabet, every CFL is regular (this was first observed by Ginsburg and Rice in 1962 [14] without relying on Parikh's theorem).…”
Section: Introductionmentioning
confidence: 99%
“…This question is related to the well-known notions of Parikh image and Parikh equivalence [Par66], which have been extensively investigated in the literature (e.g., [Gol77,AÉI02]) even for the connections of semilinear sets [Huy80] and with other fields of investigation as, e.g., Presburger Arithmetics [GS66], Petri Nets [Esp97], logical formulas [VSS05], formal verification [To10a].…”
Section: Introductionmentioning
confidence: 99%