Complexity and Dimension (1996)
| Citations: | 2 - 1 self |
BibTeX
@MISC{Cucker96complexityand,
author = {Felipe Cucker and Pascal Koiran and Martín Matamala and Ecole Normale Superieure},
title = {Complexity and Dimension},
year = {1996}
}
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Abstract
Introduction 2 Keywords: algebraic decision trees -- sparse sets -- computational complexity. 1 Introduction In 1977 Berman and Hartmanis ([1]) conjectured that all NP-complete sets are polynomially isomorphic. Should this conjecture be proved, we would have as a consequence that no "small" NP-complete set exists in a precise sense of the word "small". Denote by \Sigma the set f0; 1g and by \Sigma the set of all finite sequences of elements in \Sigma. A set S ` \Sigma is said to be sparse when there is a polynomial p such that for all n 2 IN the subset S n of all elements in S having size n has cardinality at most p(n). If the Berman-Hartmanis conjecture is
Citations
| 325 | On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines - Blum, Shub, et al. - 1989 |
| 148 | On isomorphisms and density of NP and other complete sets - Berman, Hartmanis - 1977 |
| 94 | Sparse complete sets for NP: Solution of a conjecture of berman and hartmanis - Mahaney - 1982 |
| 24 | Computing over the reals with addition and order - Koiran - 1993 |
| 20 | Computing over the real with addition and order: higher complexity classes - Cucker, Koiran - 1995 |
| 13 | A note on a P 6=NP result for a restricted class of real machines - Meer - 1992 |
