On the decidability of connectedness constraints in 2D and 3D Euclidean spaces

Authors:
Roman Kontchakov;Yavor Nenov;Ian Pratt-Hartmann;Michael Zakharyaschev
Affiliations:
Department of Computer Science and Information Systems, Birkbeck College London, UK;School of Computer Science, University of Manchester, UK;School of Computer Science, University of Manchester, UK;Department of Computer Science and Information Systems, Birkbeck College London, UK
Venue:
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Year:
2011

Citing 3
Cited 3

Recognizing string graphs in NP

Journal of Computer and System Sciences - STOC 2002
Efficient methods for qualitative spatial reasoning

Journal of Artificial Intelligence Research
On the decidability of connectedness constraints in 2D and 3D Euclidean spaces

IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two

On the decidability of connectedness constraints in 2D and 3D Euclidean spaces

IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Topological Logics with Connectedness over Euclidean Spaces

ACM Transactions on Computational Logic (TOCL)
Transition constraints: a study on the computational complexity of qualitative change

IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates, as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of reasoning varies dramatically depending on the dimension of the space and on the type of regions considered. For example, the logic with the interior-connectedness predicate (and without contact) is undecidable over polygons or regular closed sets in R2, EXPTIME-complete over polyhedra in R3, and NP-complete over regular closed sets in R3.