2010 **Abstract:** Summary. This paper presents the complexity of finding the multiset of rules in a P system in such a way to have a maximal number of rules applied. It is proved that the decision version of this problem is NP-complete. We study a number of subproblems obtained by considering that a rule can be applied at most once, and by considering the number of objects in the alphabet of the membrane as being fixed. When considering P systems with simple rules, the corresponding decision problem is in P. When considering P …

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“…We start with the remark that several attempts were done to express the maximally parallel choice of rules using Diophantine equations or ILP. In [2,55] a simple variant of ILP was used (corresponding to the equations (1a) below and variable sum as maximization function). However, in this case only maximally parallel rulesets having a maximal number of rules are obtained.…”

confidence: 99%

“…The same results can be easily obtained using formal powers associated to context-free languages. In this case, the language LN = r p 1 r q 2 | p + q = N is regular and the generation function for LN is q0 = 1/(1 − x) 2 . By expanding q0 to acquire the n-th coefficient we obtain that [x n ]q0 = n + 1, which is the function to compute N BV ariants(Π, C, max) = N + 1.…”

confidence: 99%