The Solution of SAT Problems Using Ternary Vectors and Parallel Processing

The Solution of SAT Problems Using Ternary Vectors and Parallel Processing This paper will show a new approach to the solution of SAT-problems. It has been based on the isomorphism between the Boolean algebras of finite sets and the Boolean algebras of logic functions depending on a finite number of binary variables. [Ternary vectors] are the main data structure representing sets of Boolean vectors. The respective set operations (mainly the [complement] and the [intersection]) can be executed in a [bit-parallel] way (64 bits at present), but additionally also on different processors working in parallel. Even a hierarchy of processors, a small set of processor cores of a single CPU, and the huge number of cores of the GPU has been taken into consideration. There is no need for any search algorithms. The approach always finds [all] solutions of the problem without consideration of special cases (such us [no solution, one solution, all solutions]). It also allows to include problem-relevant knowledge into the problem-solving process at an early point of time. Very often it is possible to use ternary vectors directly for the modeling of a problem. Some examples are used to illustrate the efficiency of this approach (Sudoku, Queen's problems on the chessboard, node bases in graphs, graph-coloring problems, Hamiltonian and Eulerian paths etc.).