Small P Systems Defining Non-semilinear Sets

  • Artiom AlhazovEmail author
  • Rudolf Freund
Part of the Emergence, Complexity and Computation book series (ECC, volume 12)


We present a number of tiny P systems generating or accepting nonsemilinear sets of (vectors of) natural numbers with very small numbers of rules, even for 1, 2, 3, 4, and 5 rules, depending on the particular model and the additional features used in these systems. Among the models we consider are P systems with target agreement and target selection, P systems with promoters and inhibitors, catalytic and purely catalytic P systems with normal catalysts or bi-stable catalysts. We then improve the results for catalytic (purely catalytic) P systems: 14 rules for generating a non-semilinear vector set and 29 rules for generating a non-semilinear number set are sufficient when allowing only the minimal number of two (three) catalysts; only 23 rules are needed if we allow more catalysts, i.e., five (seven) catalysts. Moreover,we introduce the new concept of toxic objects, objects that must not stay idle as otherwise the computation is abandoned without yielding a result. P systems of various kinds using toxic objects allow for smaller descriptional complexity, especially for smaller numbers of rules, as trap rules can be avoided.


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinăuMoldova
  2. 2.Faculty of InformaticsVienna University of TechnologyViennaAustria

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