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

P systems are a class of distributed parallel computing devices inspired by some basic behaviors of biological membranes, which have the restriction that each rule is executed in exactly one time unit. However, it is natural to consider the systems without the time restriction on each rule since biochemical reactions in biological systems are inherently parallel and have different reaction rates, and the execution time of biochemical reactions is unpredictably sensitive to environmental factors. In this work, we construct a family of P systems with proteins on membranes and membrane division that are “robust” against the execution time of rules. Specifically, we present a time-free uniform solution to the QSAT problem by using P systems with proteins on membranes and membrane division in the sense that the execution time of the involved rules has no influence on the correctness of the solution.