Abstract
It is well known that certain language families generated by cooperating distributed (CD) grammar systems can be characterized in terms of context-free random context grammars. In particular, the language families generated by CD grammar systems working in the t- and -modes of derivation obey a characterization in terms of ET0L systems, or equivalently by context-free disjoint forbidding random context grammars, and of context-free random context grammars with appearance checking, respectively. Now the question arises whether or not other random context like language families can be characterized in terms of CD grammar systems. We positively answer this question, proving that there are derivation modes for CD grammar systems, namely the negated versions of the aforementioned modes, which precisely characterize the family of context-free disjoint forbidding random context languages and that of languages generated by context-free random context grammars without appearance checking. In passing we show that every language generated by a context-free random context grammar without appearance checking can also be generated by a context-free recurrent programmed grammar without appearance checking, and vice versa.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bordihn, H.: On the number of components in cooperating distributed grammar systems. Theoretical Computer Science 330(2), 195–204 (2005)
Bordihn, H., Csuhaj-Varjú, E.: On competence and completeness in CD grammar systems. Acta Cybernetica 12, 347–360 (1996)
Bordihn, H., Csuhaj-Varjú, E., Dassow, J.: CD grammar systems versus L systems. In: Păun, G., Salomaa, A. (eds.) Grammatical Model of Multi-Agent Systems, Gordon and Breach, pp. 18–32 (1999)
Bordihn, H., Holzer, M.: Grammar systems with negated conditions in their cooperation protocols. Journal of Universal Computer Science 6(12), 1165–1184 (2000)
Csuhaj-Varjú, E., Dassow, J.: On cooperating/distributed grammar systems. Journal of Information Processing and Cybernetics (formerly: EIK) 26(1/2), 49–63 (1990)
Csuhaj-Varjú, E., Dassow, J., Kelemen, J., Păun, G.: Grammar Systems: A Grammatical Approach to Distribution and Cooperation, Grodon and Breach (1994)
Dassow, J., Păun, G., Rozenberg, G.: Grammar systems. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 2, pp. 155–213. Springer, Heidelberg (1997)
Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. In: EATCS Monographs in Theoretical Computer Science, vol. 18. Springer, Heidelberg (1989)
Ewert, S., van der Walt, A.P.J.: Generating pictures using random forbidding context. International Journal of Pattern Recognition and Ariticial Intelligence 12(7), 939–950 (1998)
Ewert, S., van der Walt, A.P.J.: Generating pictures using random permitting context. International Journal of Pattern Recognition and Ariticial Intelligence 13(3), 339–355 (1999)
Fernau, H.: Membership for 1-limited ET0L languages is not decidable. Journal of Information Processing and Cybernetics (formerly: EIK) 30(4), 191–211 (1994)
Fernau, H.: A predicate for separating language classes. Bulletin of the European Association for Theoretical Computer Science 56, 96–97 (1995)
Fernau, H., Freund, R., Holzer, M.: Hybrid modes in cooperating distributed grammar systems: internal versus external hybridization. Theoretical Computer Science 259(1–2), 405–426 (2001)
Fernau, H., Holzer, M., Freund, R.: Bounding resources in cooperating distributed grammar systems. In: Bozapalidis, S. (ed.) Proceedings of the 3rd International Conference Developments in Language Theory, Aristotle University of Thessaloniki, Thessalomiki, Greece, July 1997, pp. 261–272 (1997)
Fernau, H., Wätjen, D.: Remarks on regulated limited ET0L systems and regulated context-free grammars. Theoretical Computer Science 194, 35–55 (1998)
Meersman, R., Rozenberg, G.: Cooperating grammar systems. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 364–374. Springer, Heidelberg (1978)
Mitrana, V.: Hybrid cooperating/distributed grammar systems. Computers and Artificial Intelligence 12(1), 83–88 (1993)
Penttonen, M.: ET0L-grammars and N-grammars. Information Processing Letters 4(1), 11–13 (1975)
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)
van der Walt, A.P.J.: Random context languages. In: Freiman, C.V., Griffith, J.E., Rosenfeld, J.L. (eds.) Proceedings of the IFIP Congress 71, Ljubljana, Yugoslavia, August 1971, vol. 1, pp. 66–68. North-Holland, Amsterdam (1971)
von Solms, S.H.: On T0L languages over terminals. Information Processing Letters 3(3), 69–70 (1975)
von Solms, S.H.: Some notes on ET0L-languages. International Journal on Computer Mathematics 5, 285–296 (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bordihn, H., Holzer, M. (2008). Random Context in Regulated Rewriting Versus Cooperating Distributed Grammar Systems. In: Martín-Vide, C., Otto, F., Fernau, H. (eds) Language and Automata Theory and Applications. LATA 2008. Lecture Notes in Computer Science, vol 5196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88282-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-88282-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88281-7
Online ISBN: 978-3-540-88282-4
eBook Packages: Computer ScienceComputer Science (R0)