---
title: "QCSP Made Practical by Virtue of Restricted Quantification"
authors:
  - "Marco Benedetti"
  - "Arnaud Lallouet"
  - "Jérémie Vautard"
doi: ""
url: "https://ijcai.org/proceedings/2007/4"
pdf: "https://ijcai.org/proceedings/2007/0004.pdf"
venue: "Proceedings of the Twentieth International Joint Conference on Artificial Intelligence"
year: 2007
pages: "38-42"
track: ""
keywords:
---

# QCSP Made Practical by Virtue of Restricted Quantification

Marco Benedetti, Arnaud Lallouet, Jérémie Vautard

*Proceedings of the Twentieth International Joint Conference on Artificial Intelligence*, pages 38-42.

## Abstract

The QCSP+ language we introduce extends the framework of Quantified Constraint Satisfaction Problems (QCSPs) by enabling us to neatly express restricted quantifications via a chain of nested CSPs to be interpreted as alternately conjuncted and disjuncted. Restricted quantifiers turn out to be a convenient solution to the crippling modeling issues we encounter in QCSP and — surprisingly — they help to reuse propagation technology and to prune the search space. Our QCSP+ solver — which also handles arithmetic and global constraints — exhibits state-of-the-art performances.