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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 ...
The time bound for this algorithm is dominated by the time to solve a sequence of 2-satisfiability instances that are closely related to each other, and Ramnath (2004) shows how to solve these related instances more quickly than if they were solved independently from each other, leading to a total time bound of O(n 3) for the sum-of-diameters ...
The basic backtracking algorithm runs by choosing a literal, assigning a truth value to it, simplifying the formula and then recursively checking if the simplified formula is satisfiable; if this is the case, the original formula is satisfiable; otherwise, the same recursive check is done assuming the opposite truth value.
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.
In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.
Indeed, multiplying each equation of the second auxiliary system by , adding with the corresponding equation of the first auxiliary system and using the representation = +, we immediately see that equations number 2 through n of the original system are satisfied; it only remains to satisfy equation number 1.
Unit propagation of a literal can be performed efficiently by scanning only the list of clauses containing the variable of the literal. More precisely, the total running time for doing unit propagation for all unit clauses is linear in the size of the set of clauses.
Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [ 2 ] [ 3 ] [ 4 ] Iterative relaxation of solutions is commonly dubbed smoothing because with certain equations, such as Laplace's equation , it resembles repeated application of a local ...