Related papers: Parity Decision Tree Complexity and 4-Party Commun…
The FO Model Counting problem (FOMC) is the following: given a sentence $\Phi$ in FO and a number $n$, compute the number of models of $\Phi$ over a domain of size $n$; the Weighted variant (WFOMC) generalizes the problem by associating a…
We present a new example of a partial boolean function whose one-way quantum communication complexity is exponentially lower than its one-way classical communication complexity. The problem is a natural generalisation of the previously…
Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow…
We prove a complexity dichotomy for a class of counting problems expressible as bipartite 3-regular Holant problems. For every problem of the form $\operatorname{Holant}\left(f\mid =_3 \right)$, where $f$ is any integer-valued ternary…
Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been…
In communication complexity the input of a function $f:X\times Y\rightarrow Z$ is distributed between two players Alice and Bob. If Alice knows only $x\in X$ and Bob only $y\in Y$, how much information must Alice and Bob share to be able to…
The sensitivity conjecture which claims that the sensitivity complexity is polynomially related to block sensitivity complexity, is one of the most important and challenging problem in decision tree complexity theory. Despite of a lot of…
We consider a quantum and classical version multi-party function computation problem with $n$ players, where players $2, \dots, n$ need to communicate appropriate information to player 1, so that a "generalized" inner product function with…
We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…
We study the effect that the amount of correlation in a bipartite distribution has on the communication complexity of a problem under that distribution. We introduce a new family of complexity measures that interpolates between the two…
$\newcommand{\F}{\mathbb{F}}$We study the Boolean function parameters sensitivity ($s$), block sensitivity ($bs$), and alternation ($alt$) under specially designed affine transforms. For a function $f:\F_2^n\to \{0,1\}$, and $A=Mx+b$ for $M…
Sensitivity \cite{CD82,CDR86} and block sensitivity \cite{Nisan91} are two important complexity measures of Boolean functions. A longstanding open problem in decision tree complexity, the "Sensitivity versus Block Sensitivity" question,…
We introduce a restriction of the classical 2-party deterministic communication protocol where Alice and Bob are restricted to using only comparison functions. We show that the complexity of a function in the model is, up to a constant…
In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function $f$ on $n=2^k$ bits defined by a complete binary tree…
This work establishes conditional lower bounds for average-case {\em parity}-counting versions of the problems $k$-XOR, $k$-SUM, and $k$-OV. The main contribution is a set of self-reductions for the problems, providing the first specific…
A divide-and-conquer cryptanalysis can often be mounted against some keystream generators composed of several (nonlinear) independent devices combined by a Boolean function. In particular, any parity-check relation derived from the periods…
We describe a communication game, and a conjecture about this game, whose proof would imply the well-known Sensitivity Conjecture asserting a polynomial relation between sensitivity and block sensitivity for Boolean functions. The author…
We study the power of randomness in the Number-on-Forehead (NOF) model in communication complexity. We construct an explicit 3-player function $f:[N]^3 \to \{0,1\}$, such that: (i) there exist a randomized NOF protocol computing it that…
Information-theoretic methods have proven to be a very powerful tool in communication complexity, in particular giving an elegant proof of the linear lower bound for the two-party disjointness function, and tight lower bounds on…
Learning parity functions is a canonical problem in learning theory, which although computationally tractable, is not amenable to standard learning algorithms such as gradient-based methods. This hardness is usually explained via…