Computational complexity of diagram satisfaction in Euclidean geometry

Authors:
Nathaniel Miller
Affiliations:
Department of Mathematical Sciences, University of Northern Colorado, Greeley, CO
Venue:
Journal of Complexity
Year:
2006

Citing 2
Cited 0

On the computational complexity and geometry of the first-order theory of the reals. Par I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals

Journal of Symbolic Computation
Introduction To Automata Theory, Languages, And Computation

Introduction To Automata Theory, Languages, And Computation

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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.