Evolving by Maximizing the Number of Rules: Complexity Study
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This paper presents the complexity of finding a 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 systems having only two types of objects, and P systems in which a rule is applied at most once, their corresponding decision problems are NP-complete. We compare these results with those obtained for maxO evolution.
KeywordsDecision Problem Turing Machine Knapsack Problem Simple Rule Conjunctive Normal Form
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