On the number of components and clusters of non-returning parallel communicating grammar systems

E. Csuhaj-Varjú, György Vaszil

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages121-134
Number of pages14
Volume6808 LNCS
DOIs
Publication statusPublished - 2011
Event13th International Workshop of Descriptional Complexity of Formal Systems, DCFS 2011 - Giessen/Limburg, Germany
Duration: Jul 25 2011Jul 27 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6808 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other13th International Workshop of Descriptional Complexity of Formal Systems, DCFS 2011
CountryGermany
CityGiessen/Limburg
Period7/25/117/27/11

Fingerprint

Number of Components
Number of Clusters
Grammar
Necessary
Recursively Enumerable Languages
Query
Sufficient
Unary
Completeness

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Csuhaj-Varjú, E., & Vaszil, G. (2011). On the number of components and clusters of non-returning parallel communicating grammar systems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6808 LNCS, pp. 121-134). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6808 LNCS). https://doi.org/10.1007/978-3-642-22600-7_10

On the number of components and clusters of non-returning parallel communicating grammar systems. / Csuhaj-Varjú, E.; Vaszil, György.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6808 LNCS 2011. p. 121-134 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6808 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Csuhaj-Varjú, E & Vaszil, G 2011, On the number of components and clusters of non-returning parallel communicating grammar systems. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 6808 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6808 LNCS, pp. 121-134, 13th International Workshop of Descriptional Complexity of Formal Systems, DCFS 2011, Giessen/Limburg, Germany, 7/25/11. https://doi.org/10.1007/978-3-642-22600-7_10
Csuhaj-Varjú E, Vaszil G. On the number of components and clusters of non-returning parallel communicating grammar systems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6808 LNCS. 2011. p. 121-134. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-22600-7_10
Csuhaj-Varjú, E. ; Vaszil, György. / On the number of components and clusters of non-returning parallel communicating grammar systems. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6808 LNCS 2011. pp. 121-134 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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