Related papers: Information complexity is computable
We characterize the communication complexity of the following distributed estimation problem. Alice and Bob observe infinitely many iid copies of $\rho$-correlated unit-variance (Gaussian or $\pm1$ binary) random variables, with unknown…
Communication complexity is the amount of communication needed to compute a function when the function inputs are distributed over multiple parties. In its simplest form, one-way communication complexity, Alice and Bob compute a function…
It is known that the normalized algorithmic information distance $N$ is not computable and not semicomputable. We show that for all $\epsilon < 1/2$, there exist no semicomputable functions that differ from $N$ by at most~$\epsilon$.…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
Suppose that Alice and Bob are given each an infinite string, and they want to decide whether their two strings are in a given relation. How much communication do they need? How can communication be even defined and measured for infinite…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
Computational problems can be classified according to their algorithmic complexity, which is defined based on how the resources needed to solve the problem, e.g. the execution time, scale with the problem size. Many problems in…
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…
The authors discuss information-based complexity theory, which is a model of finite-precision computations with real numbers, and its applications to numerical analysis.
We prove that every online learnable class of functions of Littlestone dimension $d$ admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the…
The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($\Phi$) in the brain is…
We obtain new separation results for the two-party external information complexity of boolean functions. The external information complexity of a function $f(x,y)$ is the minimum amount of information a two-party protocol computing $f$ must…
We outline a method to estimate the value of computation for a flexible algorithm using empirical data. To determine a reasonable trade-off between cost and value, we build an empirical model of the value obtained through computation, and…
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…
Accurate information processing is crucial both in technology and in nature. To achieve it, any information processing system needs an initial supply of resources away from thermal equilibrium. Here we establish a fundamental limit on the…
We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
A measure for the complexity of a differentiable function f(x) on an interval is introduced. It is based on approximations of the function by piecewise constant functions. The measure takes into account the quality of the approximation and…
It is folklore particularly in numerical and computer sciences that, instead of solving some general problem f:A->B, additional structural information about the input x in A (that is any kind of promise that x belongs to a certain subset A'…
For any $\{0,1\}$-valued function $f$, its \emph{$n$-folded XOR} is the function $f^{\oplus n}$ where $f^{\oplus n}(X_1, \ldots, X_n) = f(X_1) \oplus \cdots \oplus f(X_n)$. Given a procedure for computing the function $f$, one can apply a…