Short proofs for tricky formulas
Acta Informatica
On the complexity of cutting-plane proofs
Discrete Applied Mathematics
Many hard examples for resolution
Journal of the ACM (JACM)
On selecting a satisfying truth assignment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Noise strategies for improving local search
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
The symmetry rule in propositional logic
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Backtrack Searching in the Presence of Symmetry
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Symmetry breaking and fault tolerance in boolean satisfiability
Symmetry breaking and fault tolerance in boolean satisfiability
| Hi-index | 0.00 |
We show that a conjunctive normal form (CNF) formula F is unsatisfiable if and only if there is a set of points of the Boolean space that is stable with respect to F. So testing the satisfiability of a CNF formula reduces to looking for a stable set of points (SSP). We give some properties of SSPs and describe a simple algorithm for constructing an SSP for a CNF formula. Building an SSP can be viewed as a “natural” way of search space traversal. This naturalness of search space examination allows one to make use of the regularity of CNF formulas to be checked for satisfiability. We illustrate this point by showing that if a CNF F formula is symmetric with respect to a group of permutations, it is very easy to make use of this symmetry when constructing an SSP. As an example, we show that the unsatisfiability of pigeon-hole CNF formulas can be proven by examining only a set of points whose size is quadratic in the number of holes. Finally, we introduce the notion of an SSP with excluded directions and sketch a procedure of satisfiability testing based on the construction of such SSPs.