Abstract
We study the generative power of CD grammar systems (CDGSs) that use a cooperation protocol based on the level of competence on a sentential form — and the competence of their components does not increase during rewriting. A component of a CDGS is k-competent on a sentential form if it can rewrite exactly k different nonterminals appearing in that string. A CDGS with components that are nonincreasing in competence works in =k-competence mode of derivation if no k-competent component can ever become l-competent, for some l > k. We introduce a static and a dynamic definition to impose this restriction, and we relate the generative power of such CDGSs working either in a sequential or in a parallel manner and according to the aforementioned cooperation protocol, for various k, with that of context-free forbidding random context grammars, (random context) ET0L systems, and context-free programmed grammars with appearance checking.
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References
Meersman, R., Rozenberg, G.: Cooperating Grammar Systems. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 364–374. Springer, Heidelberg (1978)
Csuhaj–Varjú, E., Dassow, J.: On Cooperating Distributed Grammar Systems. Journal of Information Processing and Cybernetics EIK 26, 49–63 (1990)
Csuhaj–Varjú, E., Dassow, J., Kelemen, J., Păun, G.: Grammar Systems: A Grammatical Approach to Distribution and Cooperation. Topics in Computer Mathematics, vol. 5. Gordon and Breach, London (1994)
Dassow, J., Păun, G., Rozenberg, G.: Grammar Systems. In: [13], vol. 2, ch. 4, pp. 155–213 (1997)
Bordihn, H., Csuhaj–Varjú, E.: On Competence and Completeness in CD Grammar Systems. Acta Cybernetica 12, 347–361 (1996)
ter Beek, M.H., Csuhaj–Varjú, E., Holzer, M., Vaszil, G.: On Competence in CD Grammar Systems. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 76–88. Springer, Heidelberg (2004)
ter Beek, M.H., Csuhaj–Varjú, E., Holzer, M., Vaszil, G.: On Competence in CD Grammar Systems with Parallel Rewriting. International Journal of Foundations of Computer Science 18, 1425–1439 (2007)
Csuhaj–Varjú, E., Dassow, J., Holzer, M.: CD Grammar Systems with Competence Based Entry Conditions in their Cooperation Protocols. International Journal of Computer Mathematics 83, 159–169 (2006)
von Solms, S.H.: Some Notes on ET0L-languages. International Journal of Computer Mathematics 5, 285–296 (1975)
Bordihn, H., Holzer, M.: Grammar Systems with Negated Conditions in their Cooperation Protocols. Journal of Universal Computer Science 6, 1165–1184 (2000)
Fernau, H., Wätjen, D.: Remarks on Regulated Limited ET0L Systems and Regulated Context-Free Grammars. Theoretical Computer Science 194, 35–55 (1998)
Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. EATCS Monographs in Theoretical Computer Science, vol. 18. Springer, Berlin (1989)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 1-3. Springer, Berlin (1997)
Bordihn, H., Holzer, M.: Personal communication
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ter Beek, M.H., Csuhaj-Varjú, E., Holzer, M., Vaszil, G. (2011). Cooperating Distributed Grammar Systems: Components with Nonincreasing Competence. In: Kelemen, J., Kelemenová, A. (eds) Computation, Cooperation, and Life. Lecture Notes in Computer Science, vol 6610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20000-7_7
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DOI: https://doi.org/10.1007/978-3-642-20000-7_7
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