Related papers: BPP is in NP and coNP
This article has been withdrawn due to an error in a proof of the main result.
This paper has been withdrawn by the authors due to a crucial gap in the estimates for m>=4.
Motivated by the fact that information is encoded and processed by physical systems, the P versus NP problem is examined in terms of physical processes. In particular, we consider P as a class of deterministic, and NP as nondeterministic,…
The open question, P=NP?, was presented by Cook (1971). In this paper, a proof that P is not equal to NP is presented. In addition, it is shown that P is not equal to the intersection of NP and co-NP. Finally, the exact inclusion…
This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
This paper has been withdrawn by the authors, because of a crucial gap in the proof of the main theorem.
This paper is withdrawn due to unclearness of some notions on which the material is based.
We prove that counting the analytic Brouwer degree of rational coefficient polynomial maps in $\operatorname{Map}(\mathbb C^d, \mathbb C^d)$ -- presented in degree-coefficient form -- is hard for the complexity class $\operatorname{\sharp…
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
We consider a minimal extension of the language of arithmetic, such that the bounded formulas provably total in a suitably-defined theory \`a la Buss (expressed in this new language) precisely capture polytime random functions. Then, we…
This paper is withdrawn. We found a mistake in Lemma 4.1
Withdrawn by the authors. Since the elements within each period of function hA are not distinct, period finding cannot operate properly. Thanks to all for the comments and sorry for the inconvenience.
This paper has been withdrawn by the author due to a mistake in the section 4.
This paper has been withdrawn due to disagreement of suggested results and methods between authors.
This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).
Withdrawn paper because the results are published in math.AT/0308054 and math.AT/0308063.
This paper has been withdrawn, as all conjectures (and one claim) have been proven incorrect. Some of what remains may eventually reappear in a different context.
This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.
Withdrawn because of non-correctness. Would have implied too much to be true :-|