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

Abstract

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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.

How to cite

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Aceto, 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 -

References

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