Related papers: Improved direct sum theorem in classical communica…

This paper has been withdrawn due to a crucial theoretical and experimental error.

A strong direct product theorem states that, in order to solve k instances of a problem, if we provide less than k times the resource required to compute one instance, then the probability of overall success is exponentially small in k. In…

This paper has been withdrawn by the authors due to a fatal flaw in the central proof.

We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This…

We give a strong direct sum theorem for computing $xor \circ g$. Specifically, we show that for every function g and every $k\geq 2$, the randomized query complexity of computing the xor of k instances of g satisfies…

This paper has been withdrawn by the authors due to its publication

This paper has been withdrawn by the author(s), due a mistake of factor 1/2.

This paper has been withdrawn by the authors, because it has been made obsolete by the detailed expositions in our papers in arXiv:0812.4885 (the mathematics part) and arXiv:0812.4737 (the economics part).

The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.

Withdrawn; replaced by longer, more detailed paper quant-ph/0010065.

Set-disjointness problems are one of the most fundamental problems in communication complexity and have been extensively studied in past decades. Given its importance, many lower bound techniques were introduced to prove communication lower…

This paper has been withdrawn by the author, due an error in claim 1.

This article is withdrawn because of a mistake in the main result of the paper.

This paper was withdrawn by the author due to a fatal error.

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.

The paper has been withdrawn by the author, due a gap in the proof of Theorem 6.1. The gap was discovered by M. Van den Bergh. Theorem 6.1 is used to prove the main result of the paper, namely Theorem 0.7 (decomposition in arbitrary…

Withdrawn by authors.

This paper has been withdrawn by the auther due to an error

Administratively withdrawn.