tokens: For instance , I ca n't see what precludes decision problems from being considered NP-hard optimization problems - if you consider , say , the MAX-CNF-SAT problem with the solutions being scored as floor(k/N) , where k is the number of satisfied clauses and N is the total number of clauses in the instance ( which is clearly computable in polynomial time ) , then any valuation which yields a 1 in this formula will have to satisfy the whole formula .
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Function O O B-Variable O O O O O O O B-Variable O O O O O O O O O O O O O O O O O O O O O O O O O B-Value O O O O O O O O O O O