Journal of Symbolic Computation
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Diagrams'06 Proceedings of the 4th international conference on Diagrammatic Representation and Inference
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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.