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The Parikh Property for Weighted Context-Free Grammars

Authors Pierre Ganty , Elena Gutiérrez

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Author Details

Pierre Ganty
  • IMDEA Software Institute, Madrid, Spain
Elena Gutiérrez
  • IMDEA Software Institute, Madrid, Spain, Universidad Politécnica de Madrid, Spain

Funding

  • Ganty, Pierre: Supported by the Spanish Ministry of Economy and Competitiveness project No. TIN2015-71819-P, RISCO - RIgorous analysis of Sophisticated COncurrent and distributed systems, and by a Ramón y Cajal fellowship RYC-2016-20281.
  • Gutiérrez, Elena: Supported by BES-2016-077136 grant from the Spanish Ministry of Economy, Industry and Competitiveness, and by RISCO - RIgorous analysis of Sophisticated COncurrent and distributed systems.

Cite As Get BibTex

Pierre Ganty and Elena Gutiérrez. The Parikh Property for Weighted Context-Free Grammars. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.FSTTCS.2018.32

Abstract

Parikh's Theorem states that every context-free grammar (CFG) is equivalent to some regular CFG when the ordering of symbols in the words is ignored. The same is not true for the so-called weighted CFGs, which additionally assign a weight to each grammar rule. If the result holds for a given weighted CFG G, we say that G satisfies the Parikh property. We prove constructively that the Parikh property holds for every weighted nonexpansive CFG. We also give a decision procedure for the property when the weights are over the rationals.

Subject Classification

ACM Subject Classification
  • Theory of computation → Grammars and context-free languages
Keywords
  • Weighted Context-Free Grammars
  • Algebraic Language Theory
  • Parikh Image

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