Electronic Colloquium on Computational Complexity on Rank vs. Communication Complexity
نویسنده
چکیده
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, for help
منابع مشابه
On Rank vs. Communication Complexity
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.
متن کاملSome notes on two lower bound methods for communication complexity
We compare two methods for proving lower bounds on standard two-party model of communication complexity, the Rank method and Fooling set method. We present bounds on the number of functions f(x, y), x, y ∈ {0, 1}n, with rank of size k and fooling set of size at least k, k ∈ [1, 2n]. Using these bounds we give a novel proof that almost all Boolean functions f are hard, i.e., the communication co...
متن کاملExponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity
There are three different types of nondeterminism in quantum communication: i) NQP-communication, ii) QMA-communication, and iii) QCMA-communication. In this paper we show that multiparty NQP-communication can be exponentially stronger than QCMA-communication. This also implies an exponential separation with respect to classical multiparty nondeterministic communication complexity. We argue tha...
متن کاملAn additive combinatorics approach to the log-rank conjecture in communication complexity
For a {0, 1}-valued matrixM let CC(M) denote the deterministic communication complexity of the boolean function associated with M . The log-rank conjecture of Lovász and Saks [FOCS 1988] states that CC(M) ≤ logc(rank(M)) for some absolute constant c where rank(M) denotes the rank of M over the field of real numbers. We show that CC(M) ≤ c · rank(M)/ log rank(M) for some absolute constant c, ass...
متن کاملMonotone Rank and Separations in Computational Complexity
In the paper, we introduce the concept of monotone rank, and using it as a powerful tool, we obtain several important and strong separation results in computational complexity. – We show a super-exponential separation between monotone and non-monotone computation in the non-commutative model, and thus give the answer to a longstanding open problem posed by Nisan [Nis91] in algebraic complexity....
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:
دوره شماره
صفحات -
تاریخ انتشار 1994