Solving subset sum and SAT problems by reaction systems

Abstract

We study the efficiency of the reaction systems in solving NP-complete problems. Due to the fact that standard reaction systems are qualitative, in order to accomplish our aim, in this paper we consider communicating reaction systems with direct communication extended with duration for resources and a mutual exclusion relation between reactions forbidding two reactions to be used in the same step, in parallel. We show that these systems, working in a non-deterministic way, are powerful enough to provide polynomial-time solutions to the subset sum and SAT problems. We consider a semi-uniform approach by constructing a system for each instance of the subset sum and SAT problems and embedding the parameters into the constructed systems.