On Rank vs. Communication Complexity
نویسندگان
چکیده
This paper concerns the open problem of Lovász and Saks regarding the relationship between the communication complexity of a boolean function and the rank of the associated matrix. We first give an example exhibiting the largest gap known. We then prove two related theorems.
منابع مشابه
Electronic Colloquium on Computational Complexity on Rank vs. Communication Complexity
This paper concerns the open problem of Lovasz and Saks regarding the relationship between the communication complexity of a boolean function and the rank of the associated matrix. We rst give an example exhibiting the largest gap known. We then prove two related theorems. y Extended Abstract appeared in FOCS 1994. subject "MAIL ME CLEAR", body "pub/eccc/ftpmail.txt" followed by an empty line, ...
متن کاملNonnegative Rank vs. Binary Rank
Motivated by (and using tools from) communication complexity, we investigate the relationship between the following two ranks of a 0-1 matrix: its nonnegative rank and its binary rank (the log of the latter being the unambiguous nondeterministic communication complexity). We prove that for partial 0-1 matrices, there can be an exponential separation. For total 0-1 matrices, we show that if the ...
متن کاملCharacterization of Non-Deterministic Quantum Query and Quantum Communication Complexity
It is known that the classical and quantum query complexities of a total Boolean function f are polynomially related to the degree of its representing polynomial, but the optimal exponents in these relations are unknown. We show that the non-deterministic quantum query complexity of f is linearly related to the degree of a “non-deterministic” polynomial for f . We also prove a quantum-classical...
متن کاملThe Corruption Bound, Log Rank, and Communication Complexity
We prove that for every sign matrix A there is a deterministic communication protocol that uses O(corr1/4(A) log 2 rank(A)) bits of communication, where corr1/4(A) is the corruption/rectangle bound with error 1/4. This bound generalizes several of the known upper bounds on deterministic communication complexity, involving nondeterministic complexity, randomized complexity, information complexit...
متن کاملSome improved bounds on communication complexity via new decomposition of cliques
An ordered biclique partition of the complete graph Kn on n vertices is a collection of bicliques (i.e., complete bipartite graphs) such that (i) every edge of Kn is covered by at least one and at most two bicliques in the collection, and (ii) if an edge e is covered by two bicliques then each endpoint of e is in the first class in one of these bicliques and in the second class in other one. We...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electronic Colloquium on Computational Complexity (ECCC)
دوره 1 شماره
صفحات -
تاریخ انتشار 1994