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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 ...
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem.On input a formula over Boolean variables, such as "(x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the formula true, or unsatisfiable, meaning that there are no such ...
The circuit on the left is satisfiable but the circuit on the right is not. In theoretical computer science, the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether a given Boolean circuit has an assignment of its inputs that makes the output true. [1]
For every R, add clauses representing f R (x i1,...,x iq) using 2 q SAT clauses. Clauses of length q are converted to length 3 by adding new (auxiliary) variables e.g. x 2 ∨ x 10 ∨ x 11 ∨ x 12 = ( x 2 ∨ x 10 ∨ y R) ∧ ( y R ∨ x 11 ∨ x 12). This requires a maximum of q2 q 3-SAT clauses. If z ∈ L then there is a proof π such ...
MAX-SAT, and the corresponded weighted version Weighted MAX-SAT; MAX-kSAT, where each clause has exactly k variables: MAX-2SAT; MAX-3SAT; MAXEkSAT; The partial maximum satisfiability problem (PMAX-SAT) asks for the maximum number of clauses which can be satisfied by any assignment of a given subset of clauses. The rest of the clauses must be ...
The NP-completeness of NAE3SAT can be proven by a reduction from 3-satisfiability (3SAT). [2] First the nonsymmetric 3SAT is reduced to the symmetric NAE4SAT by adding a common dummy literal to every clause, then NAE4SAT is reduced to NAE3SAT by splitting clauses as in the reduction of general -satisfiability to 3SAT.