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International Workshop on Descriptional Complexity of Formal Systems

DCFS 2011: Descriptional Complexity of Formal Systems pp 121–134Cite as

On the Number of Components and Clusters of Non-returning Parallel Communicating Grammar Systems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6808))

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.

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Author information

Authors and Affiliations

  1. Computer and Automation Research Institute, Hungarian Academy of Sciences, Kende u. 13-17, H-1111, Budapest, Hungary

    Erzsébet Csuhaj-Varjú & György Vaszil

Authors
  1. Erzsébet Csuhaj-Varjú
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  2. György Vaszil
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Markus Holzer

  2. Institut für Informatik, Universität Gießen, Arndtstraße 2, 35392, Gießen, Germany

    Martin Kutrib

  3. Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, Via Comelico 39, 20135, Milano, Italy

    Giovanni Pighizzini

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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

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  • 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)

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