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Abstract: . A detailed model of a random access computation over an abstract domain is presented, and the existence of an NP-complete problem is proven under broad conditions which unify Cook's theorem and recent results in the real number model by Blum, Shub and Smale. 1. Introduction 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... (Update)
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...are especially encouraged by S. Smale s question if there are NP complete sets over the structures R lin or R lin; see [43, 44, 47]. K. Meer [43] conjectured that this is not the case, since these structures don t even own universal functions. Recently, C. Ganer...
...the real closed fields) 6.2. TheBSS theory of computation can be carried over general first order structures (as done in [FM] Go] or [Meg]) and NP complete problem can be found (see [Go] and [Meg] All the results of the preceding sections can be done in this more general...
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BibTeX entry: (Update)
Megiddo, N. A general NP-completeness theorem. In Hirsch, Marsden & Shub (1993). http://citeseer.ist.psu.edu/article/megiddo93general.html More
@inproceedings{ megiddo93general,
author = "Megiddo",
title = "A General {NP}-Completeness Theorem",
booktitle = "{SMALEFEST}: From Topology to Computation: Proceedings of the Smalefest 1993",
publisher = "Springer-Verlag",
year = "1993",
url = "citeseer.ist.psu.edu/article/megiddo93general.html" }
Citations (may not include all citations):1450 The design and analysis of computer algorithms (context) - Aho, Hopcroft et al. - 1976
534 The complexity of theorem proving procedures (context) - Cook - 1971
213 a theory of computation and complexity over the real numbers.. (context) - Blum, Shub et al. - 1989
1 Talk at the Workshop on Computational Complexity (context) - Smale - 1990
The graph only includes citing articles where the year of publication is known.
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On the Complexity of Some Geometric Problems in Unbounded Dimension - Megiddo (1990) (Correct)
A Unified Approach to Interior Point Algorithms for.. - Kojima, Megiddo.. (1991) (Correct)
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