The complexity of linear problems in fields
Journal of Symbolic Computation
An improvement of the projection operator in cylindrical algebraic decomposition
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Algorithmic algebra
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
A machine program for theorem-proving
Communications of the ACM
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Superposition modulo non-linear arithmetic
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Hi-index | 0.00 |
We present a novel decision procedure for non-linear real arithmetic: a combination of iSAT, an incomplete SMT solver based on interval constraint propagation (ICP), and an implementation of the complete cylindrical algebraic decomposition (CAD) method in the library GiNaCRA. While iSAT is efficient in finding unsatisfiability, on satisfiable instances it often terminates with an interval box whose satisfiability status is unknown to iSAT. The CAD method, in turn, always terminates with a satisfiability result. However, it has to traverse a double-exponentially large search space. A symbiosis of iSAT and CAD combines the advantages of both methods resulting in a fast and complete solver. In particular, the interval box determined by iSAT provides precious extra information to guide the CAD-method search routine: We use the interval box to prune the CAD search space in both phases, the projection and the construction phase, forming a search "tube" rather than a search tree. This proves to be particularly beneficial for a CAD implementation designed to search a satisfying assignment pointedly, as opposed to search and exclude conflicting regions.