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

  • Authors:

  • Erzsébet Csuhaj-Varjú;György Vaszil

  • Affiliations:

  • Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary;Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary

  • Venue:
  • DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
  • Year:
  • 2011

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Abstract

In this paper, we study the size complexity of nonreturning 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.