相关论文: On a conditional inequality in Kolmogorov complexi…

We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's…

We define a new notion of information cost for quantum protocols, and a corresponding notion of quantum information complexity for bipartite quantum channels, and then investigate the properties of such quantities. These are the fully…

We define the $\textit{marginal information}$ of a communication protocol, and use it to prove XOR lemmas for communication complexity. We show that if every $C$-bit protocol has bounded advantage for computing a Boolean function $f$, then…

Set-disjointness problems are one of the most fundamental problems in communication complexity and have been extensively studied in past decades. Given its importance, many lower bound techniques were introduced to prove communication lower…

We prove a strong Symmetry of Information relation for random strings (in the sense of Kolmogorov complexity) and establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a…

In this paper, a representation of the information-disturbance theorem based on the quantum Kolmogorov complexity that was defined by P. Vitanyi has been examined. In the quantum information theory, the information-disturbance relationship,…

Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the…

Determining the randomized (or distributional) communication complexity of disjointness is a central problem in communication complexity, having roots in the foundational work of Babai, Frankl, and Simon in the 1980s and culminating in the…

We study two basic graph parameters, the chromatic number and the orthogonal rank, in the context of classical and quantum exact communication complexity. In particular, we consider two types of communication problems that we call promise…

The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…

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…

A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…

We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it…

Kolmogorov complexity theory is used to tell what the algorithmic informational content of a string is. It is defined as the length of the shortest program that describes the string. We present a programming language that can be used to…

In [3] a short proof is given that some strings have maximal plain Kolmogorov complexity but not maximal prefix-free complexity. The proof uses Levin's symmetry of information, Levin's formula relating plain and prefix complexity and Gacs'…

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…

For a broad class of input-output maps, arguments based on the coding theorem from algorithmic information theory (AIT) predict that simple (low Kolmogorov complexity) outputs are exponentially more likely to occur upon uniform random…

We discuss the communication complexity of establishing a shared reference frame, in particular examining the case of aligning spatial axes via the exchange of spin-1/2 particles. Unlike previous work we allow for multiple rounds of…

Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical…

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts…