A fully equational proof of Parikh’s theorem

Luca Aceto; Zoltán Ésik; Anna Ingólfsdóttir

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2002)

  • 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 - Informatique Théorique et Applications 36.2 (2002): 129-153. <http://eudml.org/doc/244701>.

@article{Aceto2002,
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 $\mu $-term equations of continuous commutative idempotent semirings.},
author = {Aceto, Luca, Ésik, Zoltán, Ingólfsdóttir, Anna},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {Parikh’s theorem; commutative context-free languages; commutative rational languages; equational logic; varieties; complete axiomatizations; commutative idempotent semirings; algebraically complete commutative idempotent semirings; Parikh vector; context-free language},
language = {eng},
number = {2},
pages = {129-153},
publisher = {EDP-Sciences},
title = {A fully equational proof of Parikh’s theorem},
url = {http://eudml.org/doc/244701},
volume = {36},
year = {2002},
}

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 - Informatique Théorique et Applications
PY - 2002
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 $\mu $-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 semirings; Parikh vector; context-free language
UR - http://eudml.org/doc/244701
ER -

References

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