Algebraic Techniques in Communication Complexity
نویسندگان
چکیده
In this paper we study the gap between the logarithm of the rank of a matrix and its communication complexity. The main contribution of the paper relies on the algebraic interpretation of some methods which yield non constant gaps by combining, mainly via tensor products, matrices with constant gap.
منابع مشابه
Complexity Lower Bounds using Linear Algebra
We survey several techniques for proving lower bounds in Boolean, algebraic, and communication complexity based on certain linear algebraic approaches. The common theme among these approaches is to study robustness measures of matrix rank that capture the complexity in a given model. Suitably strong lower bounds on such robustness functions of explicit matrices lead to important consequences in...
متن کاملLower Bounds in Communication Complexity: A Survey
We survey lower bounds in communication complexity. Our focus is on lower bounds that work by first representing the communication complexity measure in Euclidean space. That is to say, the first step in these lower bound techniques is to find a geometric complexity measure such as rank, or the trace norm that serves as a lower bound to the underlying communication complexity measure. Lower bou...
متن کاملMatrix Rank in Communication Complexity
This lecture focuses on proving communication lower bounds using matrix rank. Similar to fooling sets and rectangle size bounds, the matrix rank technique also gives a lower bound on the number of monochromatic rectangles in any partition of X × Y but it does so in an algebraic way[1]. This makes algebraic tools available for proving communication lower bounds. We begin by solving the problem a...
متن کاملNon-Deterministic Communication Complexity of Regular Languages
The notion of communication complexity was introduced by Yao in his seminal paper [Yao79]. In [BFS86], Babai Frankl and Simon developed a rich structure of communication complexity classes to understand the relationships between various models of communication complexity. This made it apparent that communication complexity was a self-contained mini-world within complexity theory. In this thesis...
متن کاملExtension of Cube Attack with Probabilistic Equations and its Application on Cryptanalysis of KATAN Cipher
Cube Attack is a successful case of Algebraic Attack. Cube Attack consists of two phases, linear equation extraction and solving the extracted equation system. Due to the high complexity of equation extraction phase in finding linear equations, we can extract nonlinear ones that could be approximated to linear equations with high probability. The probabilistic equations could be considered as l...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Inf. Process. Lett.
دوره 56 شماره
صفحات -
تاریخ انتشار 1995