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A decision procedure using the geometry of convex sets

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Peter W. Aitchison  and
Gabor T. Herman
Peter W. Aitchison
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada.
Gabor T. Herman
Affiliation:
Department of Computer Science, State University of New York at Buffalo, Amherst, New York, U.S.A.
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Extract

Let Zn denote the set of all ordered n-tuples of integers. Let us call any finite subset of Zn a body in Zn, and any finite set of bodies in Zn a family in Zn.

Consider the following problem:

Give a decision procedure which for any family ℱ in Zn decides the following.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 21 , Issue 2 , December 1974 , pp. 199 - 206
Copyright
Copyright © University College London 1974

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References

1.Herman, G. T.. “The uniform halting problem for generalized one-state Turing machines”, Information and Control, 15 (1969), 353–367.CrossRefGoogle Scholar
2.Herman, G. T.. “Strong computability and variants of the uniform halting problem”, Zetschr. f. math. Logik and Grundlagen d. Math., 17 (1971), 115–131.CrossRefGoogle Scholar
3.Herman, G. T. and Jackowski, J. A.. “A decision procedure using discrete geometry”, Discrete Mathematics, 5 (1973), 131–144.CrossRefGoogle Scholar
4.Stoer, J. and Witzgall, C., Convexity and optimization in finite Dimensions I (Springer, Berlin, 1970).CrossRefGoogle Scholar
5.Valentine, F. A.. Convex sets (McGraw-Hill, New York, 1964).Google Scholar