52 research outputs found
Effective problem solving using SAT solvers
In this article we demonstrate how to solve a variety of problems and puzzles
using the built-in SAT solver of the computer algebra system Maple. Once the
problems have been encoded into Boolean logic, solutions can be found (or shown
to not exist) automatically, without the need to implement any search
algorithm. In particular, we describe how to solve the -queens problem, how
to generate and solve Sudoku puzzles, how to solve logic puzzles like the
Einstein riddle, how to solve the 15-puzzle, how to solve the maximum clique
problem, and finding Graeco-Latin squares.Comment: To appear in Proceedings of the Maple Conference 201
Encoding Redundancy for Satisfaction-Driven Clause Learning
Satisfaction-Driven Clause Learning (SDCL) is a recent SAT
solving paradigm that aggressively trims the search space of possible truth assignments. To determine if the SAT solver is currently exploring a dispensable part of the search space, SDCL uses the so-called positive reduct of a formula: The positive reduct is an easily solvable propositional formula that is satisfiable if the current assignment of the solver can be safely pruned from the search space. In this paper, we present two novel variants of the positive reduct that allow for even more aggressive pruning. Using one of these variants allows SDCL to solve harder problems, in particular the well-known Tseitin formulas and mutilated chessboard problems. For the first time, we are able to generate and automatically check clausal proofs for large instances of these problems
Lower estimate of the number of steps for an inverting normal algorithm and other similar algorithms
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