Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results
Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
A DPLL-Based Calculus for Ground Satisfiability Modulo Theories
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Tuning SAT Checkers for Bounded Model Checking
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
CVC: A Cooperating Validity Checker
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Design and Results of the First Satisfiability Modulo Theories Competition (SMT-COMP 2005)
Journal of Automated Reasoning
Decision Procedures: An Algorithmic Point of View
Decision Procedures: An Algorithmic Point of View
CAV'07 Proceedings of the 19th international conference on Computer aided verification
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Generalizing DPLL to Richer Logics
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
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We study the decision problem of disjunctive linear arithmetic over the reals from the perspective of computational geometry. We show that traversing the linear arrangement induced by the formula's predicates, rather than the DPLL(T) method of traversing the Boolean space, may have an advantage when the number of variables is smaller than the number of predicates (as it is indeed the case in the standard SMT-Lib benchmarks). We then continue by showing a branching heuristic that is based on approximating T-implications, based on a geometric analysis. We achieve modest improvement in run time comparing to the commonly used heuristic used by competitive solvers.