Abstract
A simple semi-conditional (SSC) grammar is a form of regulated rewriting system where the derivations are controlled either by a permitting string alone or by a forbidden string alone and is specified in the rule. The maximum length i (j, resp.) of the permitting (forbidden, resp.) strings serves as a measure of descriptional complexity known as the degree of such grammars. In addition to the degree, the numbers of nonterminals and of conditional rules are also counted into the descriptional complexity measures of these grammars. We improve on some previously obtained results on computational completeness of SSC grammars by minimizing the number of nonterminals and/or the number of conditional rules for a given degree (i, j). More specifically, we prove that every recursively enumerable language is generated by an SSC grammar of (i) degree (2, 1) with at most eight conditional rules and nine nonterminals, (ii) degree (3, 1) with at most seven conditional rules and eight nonterminals and (iii) degree (3, 1) with at most nine conditional rules and seven nonterminals.
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Acknowledgments
This research would not have been possible without a visit of L. Kuppusamy and R. O. Oladele to the first author at the University of Trier, Germany, subsidized by CIRT, Center for Informatics Research and Technology. We also like to thank the referees for carefully reading and commenting on the submitted version.
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Fernau, H., Kuppusamy, L., Oladele, R.O., Raman, I. (2018). Minimizing Rules and Nonterminals in Semi-conditional Grammars: Non-trivial for the Simple Case. In: Durand-Lose, J., Verlan, S. (eds) Machines, Computations, and Universality. MCU 2018. Lecture Notes in Computer Science(), vol 10881. Springer, Cham. https://doi.org/10.1007/978-3-319-92402-1_5
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