Under the widely believed conjecture P≠NP, NP-complete problems cannot be solved exactly using efficient polynomial time algorithms. Furthermore, any instance of a NP-complete problem can be converted to an instance of another problem in NP in polynomial time. Thus, identifying NP-complete problems is very important in algorithm design and can help computer scientists and engineers redirect their efforts towards finding approximate solutions to these problems. As a first step towards a digital library for NP-complete problems, we describe a case study involving two well-known NP-complete problems 3-SAT and CHROMATIC together with a reduction and the corresponding soundness proof in a logical framework.
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