The Link between r-contiguous Detectors and k-CNF Satisfiability

In the context of generating detectors using the r-contiguous matching rule, questions have been raised at the efficiency of the process. We show that the problem of generating r-contiguous detectors can be transformed in a k-CNF satisfiability problem. This insight allows for the wider understanding of the problem of generating r-contiguous detectors. Moreover, we apply this result to consider questions relating to the complexity of generating detectors, and when detectors are generable.