Related papers: New Separations Results for External Information
Two problems are studied in this paper. (1) How much external or internal information cost is required to compute a Boolean-valued function with an error at most $1/2-\epsilon$ for a small $\epsilon$? It is shown that information cost of…
In a recent breakthrough paper [M. Braverman, A. Garg, D. Pankratov, and O. Weinstein, From information to exact communication, STOC'13] Braverman et al. developed a local characterization for the zero-error information complexity in the…
This paper provides the first general technique for proving information lower bounds on two-party unbounded-rounds communication problems. We show that the discrepancy lower bound, which applies to randomized communication complexity, also…
We show a partial Boolean function $f$ together with an input $x\in f^{-1}\left(*\right)$ such that both $C_{\bar{0}}\left(f,x\right)$ and $C_{\bar{1}}\left(f,x\right)$ are at least $C\left(f\right)^{2-o\left(1\right)}$. Due to recent…
We introduce a new information-theoretic complexity measure $IC_\infty$ for 2-party functions which is a lower-bound on communication complexity, and has the two leading lower-bounds on communication complexity as its natural relaxations:…
While exponential separations are known between quantum and randomized communication complexity for partial functions (Raz, STOC 1999), the best known separation between these measures for a total function is quadratic, witnessed by the…
We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently…
The question of how much communication is required between collaborating parties to compute a function of their data is of fundamental importance in the fields of theoretical computer science and information theory. In this work, the focus…
We show nearly quadratic separations between two pairs of complexity measures: 1. We show that there is a Boolean function $f$ with $D(f)=\Omega((D^{sc}(f))^{2-o(1)})$ where $D(f)$ is the deterministic query complexity of $f$ and $D^{sc}$…
We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of $\epsilon$. For arbitrary functions, we obtain lower bounds and…
We give an exponential separation between one-way quantum and classical communication protocols for a partial Boolean function (a variant of the Boolean Hidden Matching Problem of Bar-Yossef et al.) Earlier such an exponential separation…
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
We show that a rate of conditional Shannon entropy reduction, characterizing the learning of an internal process about an external process, is bounded by the thermodynamic entropy production. This approach allows for the definition of an…
The information complexity of a function $f$ is the minimum amount of information Alice and Bob need to exchange to compute the function $f$. In this paper we provide an algorithm for approximating the information complexity of an arbitrary…
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the…
Communication complexity, which quantifies the minimum communication required for distributed computation, offers a natural setting for investigating the capabilities and limitations of quantum mechanics in information processing. We…
We prove a general connection between the communication complexity of two-player games and the sample complexity of their multi-player locally private analogues. We use this connection to prove sample complexity lower bounds for locally…
We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with…
We show that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings $x$ and $y$ is equal, up to logarithmic precision, to the length of the longest shared secret key that two parties, one having $x$ and the…
We provide new query complexity separations against sensitivity for total Boolean functions: a power $3$ separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power $2.22$ separation…