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Improved Descriptional Complexity Results on Generalized Forbidding Grammars

  • Henning Fernau
  • Lakshmanan Kuppusamy
  • Rufus O. Oladele
  • Indhumathi RamanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11394)

Abstract

In formal language theory, if a grammar consists of rules of the type \((r,F_r)\), where r is a context-free rule and \(F_r\) is an associated finite set of strings called the forbidding set, such that r can be applied to a string only if none of the strings in \(F_r\) is present in the string, then the grammar is said to be a generalized forbidding (GF) grammar. There are four main parameters that describe the size of a GF grammar, namely, (i) d, the maximum length of strings in the forbidding sets, (ii) i, the maximum cardinality of the forbidding sets, (iii) n, the number of nonterminals used in the grammar, and (iv) c, the number of rules with nonempty forbidding set. The family of languages described by a GF grammar of size (at most) (dinc) is denoted by GF(dinc). We study for what sizes of generalized forbidding grammars one can obtain the computational power of Turing machines. We specifically show this result for sizes (2, 6, 8, 6), (2, 5, 8, 8), (2, 4, 9, 9) and (2, 3, 20, 18). These results improve on previous results on the descriptional complexity of generalized forbidding grammars.

Keywords

Descriptional complexity in formal languages Semi-conditional grammars Generalized forbidding grammars Computational completeness 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Henning Fernau
    • 1
  • Lakshmanan Kuppusamy
    • 2
  • Rufus O. Oladele
    • 3
  • Indhumathi Raman
    • 4
    Email author
  1. 1.Abteilung Informatikwissenschaften, CIRT, Fachbereich 4, Universität TrierTrierGermany
  2. 2.School of Computer Science and EngineeringVITVelloreIndia
  3. 3.Department of Computer ScienceUniversity of IlorinIlorinNigeria
  4. 4.Department of Applied Mathematics and Computational SciencesPSG College of TechnologyCoimbatoreIndia

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