Related papers: NP-Completeness of Deterministic Communication Com…
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…
There is a close relationship between the communication complexity and information complexity of communication problems, as demonstrated by results such as Shannon's noiseless source coding theorem, and the Slepian-Wolf theorem. Here, we…
The broadcast model is widely used to describe the process of information dissemination from a single node to all nodes within an interconnected network. In this model, a graph represents the network, where vertices correspond to nodes and…
In this article I introduce a new communication theory for complex information represented as a direct graph of nodes. In addition, I introduce an application for the theory, a new radical method, embed, that can be used to update object…
The main result of this paper is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge…
We define nondeterministic communication complexity in the model of communication complexity with help of Babai, Hayes and Kimmel. We use it to prove logarithmic lower bounds on the NOF communication complexity of explicit graph functions,…
A Boolean network (BN) is a discrete dynamical system defined by a Boolean function that maps to the domain itself. A trap space of a BN is a generalization of a fixed point, which is defined as the sub-hypercubes closed by the function of…
Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output…
We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…
Shannon's information theory deliberately excludes message semantics. This paper develops a rigorous framework for semantic communication that integrates formal proof systems with Shannon-theoretic tools. We introduce an axiomatic…
We consider the message complexity of verifying whether a given subgraph of the communication network forms a tree with specific properties both in the KT-$\rho$ (nodes know their $\rho$-hop neighborhood, including node IDs) and the KT-$0$…
We study matrix completion via deep matrix factorization (a.k.a. deep linear neural networks) as a simplified testbed to examine how network depth influences training dynamics. Despite the simplicity and importance of the problem, prior…
Feasible interpolation is a general technique for proving proof complexity lower bounds. The monotone version of the technique converts, in its basic variant, lower bounds for monotone Boolean circuits separating two NP-sets to proof…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
The contemporary scientific landscape is characterized by a "curse of dimensionality," where our capacity to collect high-dimensional network data frequently outstrips our ability to computationally simulate or intuitively comprehend the…
This paper focuses on bounding the total communication complexity of collapsing protocols for multiparty pointer jumping problem ($MPJ_k^n$). Brody and Chakrabati in \cite{bc08} proved that in such setting one of the players must…
In 1979 Valiant introduced the complexity class VNP of p-definable families of polynomials, he defined the reduction notion known as p-projection and he proved that the permanent polynomial and the Hamiltonian cycle polynomial are…
Consensus is one of the most thoroughly studied problems in distributed computing, yet there are still complexity gaps that have not been bridged for decades. In particular, in the classical message-passing setting with processes' crashes,…
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…
Classical Bayesian persuasion assumes that senders fully understand how receivers form beliefs and make decisions--an assumption that rarely holds when receivers possess private information or exhibit non-Bayesian behavior. In this paper,…