An efficient time-free solution to QSAT problem using P systems with proteins on membranes

Abstract

P systems are a class of distributed parallel computing devices inspired by some basicbehaviors of biological membranes, which have the restriction that each rule is executedin exactly one time unit. However, it is natural to consider the systems without the timerestriction on each rule since biochemical reactions in biological systems are inherentlyparallel and have different reaction rates, and the execution time of biochemical reactionsis unpredictably sensitive to environmental factors. In this work, we construct a family ofPsystems with proteins on membranes and membrane division that are “robust” againstthe execution time of rules. Specifically, we present a time-free uniform solution to theQSATproblem by using Psystems with proteins on membranes and membrane division inthe sense that the execution time of the involved rules has no influence on the correctnessof the solution.