On the Trade-off Between Ambiguity and Complexity in Contextual Languages

Article type: Research Article

Authors: Kuppusamy, Lakshmanan | Mahendran, Anand | Krithivasan, Kamala

Affiliations: School of Computing Science and Engineering, VIT University, Vellore 632 014, India. [email protected] | School of Computing Science and Engineering, VIT University, Vellore 632 014, India. [email protected] | Department of Computer Science and Engineering, IIT Madras, Chennai 600 036, India. [email protected]

Note: [] Address for correspondence: School of Computing Science and Engineering, VIT University, Vellore 632 014, India.

Abstract: Contextual grammars are introduced by Solomon Marcus in 1969 based on the fundamental concept of descriptive linguistics of insertion of strings in given contexts. Internal contextual grammars are introduced by Păun and Nguyen in 1980. For contextual grammars several descriptional complexity measures and levels of ambiguity have been defined. In this paper, we analyze the trade-off between ambiguity and complexity of languages generated by internal contextual grammars. The notion of a pseudo inherently ambiguous language with respect to two complexity measures is introduced and investigated. These languages can be generated by unambiguous grammars which are minimal with respect to one measure and ambiguous if they are minimal with respect to the other measure. An open problem from [15] is solved in this framework.

Keywords: inherently ambiguous, unambiguous, descriptional complexity measures, internal contextual grammars

DOI: 10.3233/FI-2013-792

Journal: Fundamenta Informaticae, vol. 122, no. 4, pp. 315-326, 2013