Abstract Domains for Constraint Programming, with the Example of Octagons

In Constraint Programming (CP), the central notion of consistency can be defined as a fix point of some contracting operators. These operators always deal with cartesian products of domains of the same nature (real intervals, integer sets, etc), due to the cartesian nature of the CSP format. However...

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Bibliographic Details
Published in:2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing pp. 72 - 79
Main Authors: Truchet, C, Pelleau, M, Benhamou, Frédéric
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2010
Subjects:
abstract domains
Approximation methods
Artificial intelligence
Computer bugs
Concrete
Constraint programming
Lattices
Programming
Semantics
ISBN:1424498163, 9781424498161
Online Access:Get full text
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Summary:In Constraint Programming (CP), the central notion of consistency can be defined as a fix point of some contracting operators. These operators always deal with cartesian products of domains of the same nature (real intervals, integer sets, etc), due to the cartesian nature of the CSP format. However, \textit{inside} the solving process, there is no particular reason why the domains should be cartesian. In another research field, Abstract Interpretation (AI) in semantics relies on a strong and elegant theory dealing with over-approximations of variables. It allows in particular to mix abstract domains of different kinds (integer, reals...). Several numerical abstract domains for continuous variables have recently been proposed, some of them cartesian, other relational. In this article, we adapt to CP the AI definition of abstract domains. We give an abstract consistency definition, and show it extends the usual CP consistencies. We also give a general solving algorithm for abstract domains. Finally, we propose the octagon abstract domain and study its practical feasibility.
ISBN:1424498163
9781424498161
DOI:10.1109/SYNASC.2010.69