Efficient Solving of Quantified Inequality Constraints over the Real Numbers

Details Efficient Solving of Quantified Inequality Constraints over the Real Numbers Efficient Solving of Quantified Inequality Constraints over the Real Numbers

2002-11-14

arxiv.org/abs/cs/0211016v4

Computer Science

Logic in Computer Science

Scientific paper

Let a quantified inequality constraint over the reals be a formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are $\leq$ and $<$. Solving such constraints is an undecidable problem when allowing function symbols such $\sin$ or $\cos$. In the paper we give an algorithm that terminates with a solution for all, except for very special, pathological inputs. We ensure the practical efficiency of this algorithm by employing constraint programming techniques.

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