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Computational complexity of diagram satisfaction in Euclidean geometry
- Source :
-
Journal of Complexity . Apr2006, Vol. 22 Issue 2, p250-274. 25p. - Publication Year :
- 2006
-
Abstract
- Abstract: In this paper, it is shown that the problem of deciding whether or not a geometric diagram in Euclidean Geometry is satisfiable is NP-hard and in PSPACE, and in fact has the same complexity as the satisfaction problem for a fragment of the existential theory of the real numbers. The related problem of finding all of the possible (satisfiable) diagrams that can result when a segment of a diagram is extended is also shown to be NP-hard. [Copyright &y& Elsevier]
- Subjects :
- *EUCLID'S elements
*COMPUTATIONAL complexity
*REAL numbers
*POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 0885064X
- Volume :
- 22
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Complexity
- Publication Type :
- Academic Journal
- Accession number :
- 19593318
- Full Text :
- https://doi.org/10.1016/j.jco.2005.09.003