Add to ORKGWe characterize the approximate monomial complexity, sign monomial complexity , and the approximate L 1 norm of symmetric functions in terms of simple combinatorial measures of the functions. Our characterization of the approximate L 1 norm solves the main conjecture in [AFH12]. As an application of the characterization of the sign monomial complexity, we prove a conjecture in [ZS09] and provide a characterization for the unbounded-error communication complexity of symmetric-xor functions
AbstractWe study the problem of representing symmetric Boolean functions as symmetric polynomials ov...
We study how well functions over the boolean hypercube of the form f_k(x)=(lxl-k)(lxl-k-1) can be ap...
The first section starts with the basic definitions following mainly the notations of the book writt...
We characterize the approximate monomial complexity, sign monomial complexity , and the approximate ...
The sign-rank of a real matrix M is the least rank of a matrix R in which every entry has the same s...
Abstract. We study the communication complexity of symmetric XOR functions, namely functions f: {0, ...
In this paper we prove several fundamental theorems, concerning the multi--party communication compl...
AbstractA quadratic upper bound is obtained for the complexity of symbol sequences generated by symm...
AbstractThe symmetric complexity of a polynomial in n variables is defined as the number of times th...
AbstractThe multiplicative complexity of a Boolean function f is defined as the minimum number of bi...
In this thesis we consider the boolean elementary symmetric functions over a field with characterist...
Abstract—We study Boolean functions with sparse Fourier spectrum or small spectral norm, and show th...
AbstractThe communication complexity of a function f denotes the number of bits that two processors ...
AbstractThe rigidity of a matrix measures the number of entries that must be changed in order to red...
Let f : {0, 1}n → {0, 1} be a boolean function. Its associated XOR function is the two-party functio...
AbstractWe study the problem of representing symmetric Boolean functions as symmetric polynomials ov...
We study how well functions over the boolean hypercube of the form f_k(x)=(lxl-k)(lxl-k-1) can be ap...
The first section starts with the basic definitions following mainly the notations of the book writt...
We characterize the approximate monomial complexity, sign monomial complexity , and the approximate ...
The sign-rank of a real matrix M is the least rank of a matrix R in which every entry has the same s...
Abstract. We study the communication complexity of symmetric XOR functions, namely functions f: {0, ...
In this paper we prove several fundamental theorems, concerning the multi--party communication compl...
AbstractA quadratic upper bound is obtained for the complexity of symbol sequences generated by symm...
AbstractThe symmetric complexity of a polynomial in n variables is defined as the number of times th...
AbstractThe multiplicative complexity of a Boolean function f is defined as the minimum number of bi...
In this thesis we consider the boolean elementary symmetric functions over a field with characterist...
Abstract—We study Boolean functions with sparse Fourier spectrum or small spectral norm, and show th...
AbstractThe communication complexity of a function f denotes the number of bits that two processors ...
AbstractThe rigidity of a matrix measures the number of entries that must be changed in order to red...
Let f : {0, 1}n → {0, 1} be a boolean function. Its associated XOR function is the two-party functio...
AbstractWe study the problem of representing symmetric Boolean functions as symmetric polynomials ov...
We study how well functions over the boolean hypercube of the form f_k(x)=(lxl-k)(lxl-k-1) can be ap...
The first section starts with the basic definitions following mainly the notations of the book writt...