# A Fully Equational Proof of Parikh's Theorem

Luca Aceto; Zoltán Ésik; Anna Ingólfsdóttir

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 36, Issue: 2, page 129-153
- ISSN: 0988-3754

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topAceto, Luca, Ésik, Zoltán, and Ingólfsdóttir, Anna. "A Fully Equational Proof of Parikh's Theorem." RAIRO - Theoretical Informatics and Applications 36.2 (2010): 129-153. <http://eudml.org/doc/92694>.

@article{Aceto2010,

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.
},

author = {Aceto, Luca, Ésik, Zoltán, Ingólfsdóttir, Anna},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Parikh's theorem; commutative context-free languages;
commutative rational languages; equational logic; varieties;
complete axiomatizations; commutative idempotent semirings;
algebraically complete commutative idempotent semi rings.; complete axiomatizations; Parikh vector; context-free language},

language = {eng},

month = {3},

number = {2},

pages = {129-153},

publisher = {EDP Sciences},

title = {A Fully Equational Proof of Parikh's Theorem},

url = {http://eudml.org/doc/92694},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Aceto, Luca

AU - Ésik, Zoltán

AU - Ingólfsdóttir, Anna

TI - A Fully Equational Proof of Parikh's Theorem

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 2

SP - 129

EP - 153

AB -
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.

LA - eng

KW - Parikh's theorem; commutative context-free languages;
commutative rational languages; equational logic; varieties;
complete axiomatizations; commutative idempotent semirings;
algebraically complete commutative idempotent semi rings.; complete axiomatizations; Parikh vector; context-free language

UR - http://eudml.org/doc/92694

ER -

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