Abstract
In this paper, we study the size complexity of non-returning parallel communicating grammar systems. First we consider the problem of determining the minimal number of components necessary to generate all recursively enumerable languages. We present a construction which improves the currently known best bounds of seven (with three predefined clusters) and six (in the non-clustered case) to five, in both cases (having four clusters in the clustered variant). We also show that in the case of unary languages four components are sufficient. Then, by defining systems with dynamical clusters, we investigate the minimal number of different query symbols necessary to obtain computational completeness. We prove that for this purpose three dynamical clusters (which means two different query symbols) are sufficient in general, which (although the number of components is higher) can also be interpreted as an improvement in the number of necessary clusters when compared to the case of predefined clusters.
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.
Similar content being viewed by others
References
ter Beek, M.H.: Teams in grammar systems: hybridity and weak rewriting. Acta Cybernetica 12(4), 427–444 (1996)
ter Beek, M.H.: Teams in grammar systems: sub-context-free cases. In: Păun, G., Salomaa, A. (eds.) New Trends in Formal Languages. LNCS, vol. 1218, pp. 197–216. Springer, Heidelberg (1997)
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 Science Publishers, Yverdon (1994)
Csuhaj-Varjú, E., Mitrana, V.: Dynamical Teams in Eco-Grammar Systems. Fundamenta Informaticae 44(1-2), 83–94 (2000)
Csuhaj-Varjú, E., Oswald, M., Vaszil, G.: PC grammar systems with clusters of components. International Journal of Foundations of Computer Science 22(1), 203–212 (2011)
Csuhaj-Varjú, E., Păun, G., Vaszil, G.: PC grammar systems with five context-free components generate all recursively enumerable languages. Theoretical Computer Science 299(1-3), 785–794 (2003)
Csuhaj-Varjú, E., Vaszil, G.: On the size complexity of non-returning context-free PC grammar systems. In: Dassow, J., Pighizzini, G., Truthe, B. (eds.) Proceedings Eleventh International Workshop on Descriptional Complexity of Formal Systems, Electronic Proceedings in Theoretical Computer Science, vol. 3, pp. 91–101 (2009)
Dassow, J., Păun, G., Rozenberg, G.: Grammar systems. In: Salomaa, A., Rozenberg, G. (eds.) Handbook of Formal Languages, vol. II, ch. 4, pp. 155–213. Springer, Heidelberg (1997)
Fischer, P.C.: Turing machines with restricted memory access. Information and Control 9, 364–379 (1966)
Kari, L., Mateescu, A., Păun, G., Salomaa, A.: Teams in cooperating grammar systems. Journal of Experimental and Theoretical Artificial Intelligence 7, 347–359 (1995)
Lázár, K., Csuhaj-Varjú, E., Lőrincz, A., Vaszil, G.: Dynamically formed Clusters of Agents in Eco-grammar Systems. International Journal of Foundations of Computer Science 20(2), 293–311 (2009)
Mateescu, A., Mitrana, V., Salomaa, A.: Dynamical teams of cooperating grammar systems. Analele Universitatii Bucuresti. Matematica Inform. 42(43), 3–14 (1993)
Minsky, M.: Computation – Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)
Păun, G., Rozenberg, G.: Prescribed teams of grammars. Acta Informatica 31(6), 525–537 (1994)
Păun, G., Sântean, L.: Parallel communicating grammar systems: The regular case. Annals of the University of Bucharest, Mathematics-Informatics Series 38(2), 55–63 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Csuhaj-Varjú, E., Vaszil, G. (2011). On the Number of Components and Clusters of Non-returning Parallel Communicating Grammar Systems. In: Holzer, M., Kutrib, M., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2011. Lecture Notes in Computer Science, vol 6808. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22600-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-22600-7_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22599-4
Online ISBN: 978-3-642-22600-7
eBook Packages: Computer ScienceComputer Science (R0)