Generating All Circular Shifts by Context-Free Grammars in Greibach Normal Form

Peter R.J. Asveld

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

For each alphabet Σn = {a1,a2,…,an}, linearly ordered by a1 < a2 < ⋯ < an, let Cn be the language of circular or cyclic shifts over Σn, i.e., Cn = {a1a2 ⋯ an-1an, a2a3 ⋯ ana1,…,ana1 ⋯ an-2an-1}. We study a few families of context-free grammars Gn (n ≥1) in Greibach normal form such that Gn generates Cn. The members of these grammar families are investigated with respect to the following descriptional complexity measures: the number of nonterminals ν(n), the number of rules π(n) and the number of leftmost derivations δ(n) of Gn. As in the case of Chomsky normal form, these ν, π and δ are functions bounded by low-degree polynomials. However, the question whether there exists a family of grammars that is minimal w. r. t. all these measures remains open.
Original languageEnglish
Pages (from-to)1139-1149
JournalInternational journal of foundations of computer science
Volume18
Issue number6
DOIs
Publication statusPublished - Dec 2007

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Context free grammars
Polynomials

Keywords

  • Context-free grammar
  • EWI-11338
  • IR-62000
  • descriptional complexity
  • HMI-SLT: Speech and Language Technology
  • cyclic shift
  • METIS-242033
  • unambiguous grammar
  • circular shift
  • permutation
  • Greibach normal form

Cite this

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title = "Generating All Circular Shifts by Context-Free Grammars in Greibach Normal Form",
abstract = "For each alphabet Σn = {a1,a2,…,an}, linearly ordered by a1 < a2 < ⋯ < an, let Cn be the language of circular or cyclic shifts over Σn, i.e., Cn = {a1a2 ⋯ an-1an, a2a3 ⋯ ana1,…,ana1 ⋯ an-2an-1}. We study a few families of context-free grammars Gn (n ≥1) in Greibach normal form such that Gn generates Cn. The members of these grammar families are investigated with respect to the following descriptional complexity measures: the number of nonterminals ν(n), the number of rules π(n) and the number of leftmost derivations δ(n) of Gn. As in the case of Chomsky normal form, these ν, π and δ are functions bounded by low-degree polynomials. However, the question whether there exists a family of grammars that is minimal w. r. t. all these measures remains open.",
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Generating All Circular Shifts by Context-Free Grammars in Greibach Normal Form. / Asveld, Peter R.J.

In: International journal of foundations of computer science, Vol. 18, No. 6, 12.2007, p. 1139-1149.

Research output: Contribution to journalArticleAcademicpeer-review

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