Abstract
Blum, Shub, and Smale [2] formalized a model of computation over a general ring. They proved an analogue of Cook’s theorem [3] over the reals. Smale [4] has recently raised the question of existence of NP-complete problems relative to “linear” machines, i.e., machines which add, subtract, multiply by constants, and branch, depending on the sign of a number.
Parts of this work were done during a visit to IMPA, Rio de Janeiro.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A.V. Aho, J.E. Hopcroft and J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1976.
L. Blum, M. Shub, and S. Smale, “On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines, ” Bull. Amer. Math. Soc. 21 (1989), 1–46.
S.A. Cook, “The complexity of theorem proving procedures”, Proceedings of the 3rd Annual ACM Symposium on Theory of Computing (1971), pp. 151–158.
S. Smale, talk at the Workshop on Computational Complexity, IMPA, Rio de Janeiro, January, 1990.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Megiddo, N. (1999). A General NP-Completeness Theorem. In: Hirsch, M.W., Marsden, J.E., Shub, M. (eds) From Topology to Computation: Proceedings of the Smalefest. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2740-3_39
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2740-3_39
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7648-7
Online ISBN: 978-1-4612-2740-3
eBook Packages: Springer Book Archive