Sublinear P system solutions to NP-complete problems

Abstract

cP systems have been shown to very e ciently solve many NP-complete problems, i.e. in linear time. However, these solutions have been independent of each other and have not utilised the theory of reductions. This work presents a sublinear solution to k-SAT and demonstrates that k-colouring can be reduced to k-SAT in constant time. This work demonstrates that traditional reductions are e cient in cP systems and that they can sometimes produce more e cient solutions than the previous problem-speci c solutions.