Abstract
Catalytic P systems are among the first variants of membrane systems ever considered in this area. This variant of systems also features some prominent computational complexity questions, and in particular the problem of using only one catalyst in the whole system: is one catalyst enough to allow for generating all recursively enumerable sets of multisets? Several additional ingredients have been shown to be sufficient for obtaining computational completeness even with only one catalyst. In this paper, we show that one catalyst is sufficient for obtaining computational completeness if either catalytic rules have weak priority over non-catalytic rules or else instead of the standard maximally parallel derivation mode, we use the derivation mode maxobjects, i.e., we only take those multisets of rules which affect the maximal number of objects in the underlying configuration.
Highlights
Membrane systems were introduced in [10] as a multisetrewriting model of computing inspired by the structure and the functioning of the living cell
We recall the result from [2], but show a somehow much stronger result using a similar construction as in [2]: we show computational completeness for catalytic P systems with only one catalyst using the derivation mode maxobjects, i.e., we only take those multisets of rules which affect the maximal number of objects in the underlying configuration
We revisited a classical problem of computational complexity in membrane computing: can catalytic P systems working in the derivation mode max with only one catalyst in the whole system already generate all recursively enumerable sets of multisets? This problem has been standing tall for many years, and nobody has yet managed to give a positive or a negative answer to this problem
Summary
Membrane systems were introduced in [10] as a multisetrewriting model of computing inspired by the structure and the functioning of the living cell. In [2], we returned to the idea of using a priority relation on the rules, but took only a very weak form of such a priority relation: we only required that overall in the system, catalytic rules have weak priority over non-catalytic rules This means that the catalyst c must not stay idle if the current configuration contains an object a with which it may cooperate in a rule ca → cv ; all remaining objects evolve in the maximally parallel way with non-cooperative rules. We recall the result from [2], but show a somehow much stronger result using a similar construction as in [2]: we show computational completeness for catalytic P systems with only one catalyst using the derivation mode maxobjects, i.e., we only take those multisets of rules which affect the maximal number of objects in the underlying configuration
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