Improved normal form for grammars with one-sided contexts

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4 Scopus citations


Formal grammars equipped with operators for specifying the form of the context of a substring were recently studied by Barash and Okhotin ("Defining contexts in context-free grammars", LATA 2012), further extending the author's ("Conjunctive grammars", DCAGRS 2000) earlier work on propositional connectives in grammars. These grammars allow two types of context specifications: for a substring w of a string uwv, a left context operator ◁D states that u is of the form described by D, while the extended left context operator ⊴E states that uw is described by E. This paper establishes a normal form for these grammars, in which extended left contexts are never used, while left contexts may be applied only for individual symbols, so that all rules are of the form A → B1C1 &⋯& BnCn or A → a & ◁D. This eliminates circular dependencies in the grammar and allows simplifying the known parsing algorithm. Some further improvements to the algorithm accelerate it from time O(n3) to time O(n3/log n).

Original languageEnglish
Title of host publicationDescriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings
Number of pages12
StatePublished - 2013
Externally publishedYes
Event15th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2013 - London, ON, Canada
Duration: 22 Jul 201325 Jul 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8031 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2013
CityLondon, ON

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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