Abstract
Non-linear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifier-free equivalent form by means of Cylindrical Algebraic Decomposition (CAD). However, CAD restricts its input to be conjunctions and disjunctions of polynomial constraints with rational coefficients, while some applications such as camera control involve systems with arbitrary forms where time is the only universally quantified variable. In this paper, the handling of universally quantified variables is first related to the computation of inner-approximation of real relations. Algorithms for solving non-linear real constraint systems with universally quantified variables are then presented along with the theoretical framework on inner-approximation of relations supporting them. These algorithms are based on the computation of outer-approximations of the solution set of the negation of involved constraints. An application to the devising of a declarative modeller for expressing camera motion using a cinematic language is sketched, and results from a prototype are presented.
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Benhamou, F., Goualard, F. (2000). Universally Quantified Interval Constraints. In: Dechter, R. (eds) Principles and Practice of Constraint Programming – CP 2000. CP 2000. Lecture Notes in Computer Science, vol 1894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45349-0_7
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DOI: https://doi.org/10.1007/3-540-45349-0_7
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