Some notes on two lower bound methods for communication complexity
نویسنده
چکیده
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 complexity of f is greater than or equal to n, using the field Z2.
منابع مشابه
A Survey on Complexity of Integrity Parameter
Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. In this paper we discuss Integrity and its properties in vulnerability calculation. The integrity of a graph G, I(G), is defined t...
متن کاملOn the Power of Lower Bound Methods for One-Way Quantum Communication Complexity
This paper studies the three known lower bound methods for one-way quantum communication complexity, namely the Partition Tree method by Nayak, the Trace Distance method by Aaronson, and the two-way quantum communication complexity. It is shown that all these three methods can be exponentially weak for some total Boolean functions. In particular, for a large class of functions generated from Er...
متن کاملBearing Capacity of Strip Footings near Slopes Using Lower Bound Limit Analysis
Stability of foundations near slopes is one of the important and complicated problems in geotechnical engineering, which has been investigated by various methods such as limit equilibrium, limit analysis, slip-line, finite element and discrete element. The complexity of this problem is resulted from the combination of two probable failures: foundation failure and overall slope failure. The curr...
متن کاملTowards a Theory of Multiparty Information Complexity
Communication complexity seeks to characterize the complexity of computation by measuring the amount of communication that must be used by players computing the output of some function f , each of whom have only partial information about the inputs to f . The past thirty years have seen the development of a number of lower-bound techniques in communication complexity, which fall roughly into tw...
متن کاملRemarks on Graph Complexity
We revisit the notion of graph complexity introduced by Pudll ak, RR odl, and Savick y PRS]. Using their framework, we show that suuciently strong superlinear monotone lower bounds for the very special class of 2-slice functions would imply superpolynomial lower bounds for some other functions. Given an n-vertex graph G, the corresponding 2-slice function fG on n variables evaluates to zero on ...
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:
- Electronic Colloquium on Computational Complexity (ECCC)
دوره 24 شماره
صفحات -
تاریخ انتشار 2017