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More generally, one can define a weighted version of MAX-SAT as follows: given a conjunctive normal form formula with non-negative weights assigned to each clause, find truth values for its variables that maximize the combined weight of the satisfied clauses. The MAX-SAT problem is an instance of Weighted MAX-SAT where all weights are 1. [5] [6 ...
A variant of the 3-satisfiability problem is the one-in-three 3-SAT (also known variously as 1-in-3-SAT and exactly-1 3-SAT). Given a conjunctive normal form with three literals per clause, the problem is to determine whether there exists a truth assignment to the variables so that each clause has exactly one TRUE literal (and thus exactly two ...
The partial Max-SAT problem is the problem where some clauses necessarily must be satisfied (hard clauses) and the sum total of weights of the rest of the clauses (soft clauses) are to be maximized or minimized, depending on the problem. Partial Max-SAT represents an intermediary between Max-SAT (all clauses are soft) and SAT (all clauses are ...
The soft satisfiability problem (soft-SAT), given a set of SAT problems, asks for the maximum number of sets which can be satisfied by any assignment. [2] The minimum satisfiability problem. The MAX-SAT problem can be extended to the case where the variables of the constraint satisfaction problem belong the set of reals.
In the maximum-2-satisfiability problem (MAX-2-SAT), the input is a formula in conjunctive normal form with two literals per clause, and the task is to determine the maximum number of clauses that can be simultaneously satisfied by an assignment. Like the more general maximum satisfiability problem, MAX-2-SAT is NP-hard.
MAX-3SAT(B) is the restricted special case of MAX-3SAT where every variable occurs in at most B clauses. Before the PCP theorem was proven, Papadimitriou and Yannakakis [3] showed that for some fixed constant B, this problem is MAX SNP-hard. Consequently, with the PCP theorem, it is also APX-hard.
Image credits: anon #20. I learned long ago that when the wife asks if her hair / outfit / nails / new purse / whatever looks nice, the correct answer 100% of the time with no exceptions is "Yes."
[235] [236] The changes included making the essay optional (and returning the maximum score to 1600), changing all multiple-choice questions from having five answer options to four, and the removal of penalty for wrong answers (rights-only scoring).
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