## Universally Quantified Interval Constraints (2000)

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Venue: | PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING |

Citations: | 46 - 0 self |

### BibTeX

@INPROCEEDINGS{Benhamou00universallyquantified,

author = {Frédéric Benhamou and Frédéric Goualard},

title = {Universally Quantified Interval Constraints},

booktitle = {PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING},

year = {2000},

pages = {67--82},

publisher = {Springer Verlag}

}

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### 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.