Abstract
Many membrane systems (e.g. P System), including cP systems (P Systems with compound terms), have been used to solve efficiently many NP-hard problems, often 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 efficient in cP systems and that they can sometimes produce more efficient solutions than the previous problem-specific solutions.
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