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Efficient solving of large non-linear arithmetic constraint systems with complex Boolean structure. (English) Zbl 1144.68371
Summary: In order to facilitate automated reasoning about large Boolean combinations of nonlinear arithmetic constraints involving transcendental functions, we provide a tight integration of recent SAT solving techniques with interval-based arithmetic constraint solving. Our approach deviates substantially from lazy theorem proving approaches in that it directly controls arithmetic constraint propagation from the SAT solver rather than delegating arithmetic decisions to a subordinate solver. Through this tight integration, all the algorithmic enhancements that were instrumental to the enormous performance gains recently achieved in prepositional SAT solving carry over smoothly to the rich domain of non-linear arithmetic constraints. As a consequence, our approach is able to handle large constraint systems with extremely complex Boolean structure, involving Boolean combinations of multiple thousand arithmetic constraints over some thousands of variables.

68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)