Quadtrees as an Abstract Domain

doi:10.1016/j.entcs.2010.09.008

Electronic Notes in Theoretical Computer Science

Volume 267, Issue 1, 1 October 2010, Pages 89-100

https://doi.org/10.1016/j.entcs.2010.09.008 Get rights and content

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Abstract

Quadtrees have proved popular in computer graphics and spatial databases as a way of representing regions in two dimensional space. This hierarchical data-structure is flexible enough to support non-convex and even disconnected regions, therefore it is natural to ask whether this data-structure can form the basis of an abstract domain. This paper explores this question and suggests that quadtrees offer a new approach to weakly relational domains whilst their hierarchical structure naturally lends itself to representation with boolean functions.

Keywords

Weakly relational domains

abstract interpretation

quadtrees

boolean formulae

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¹: This work is supported by EPSRC projects EP/E033105/1 and EP/E034519/1.

²: Partly supported by a Royal Society Industrial Fellowship.

³: Supported by a Nuffield Science Bursary.