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Related papers: Query-to-Communication Lifting for BPP

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This paper describes a purely functional library for computing level-$p$-complexity of Boolean functions, and applies it to two-level iterated majority. Boolean functions are simply functions from $n$ bits to one bit, and they can describe…

Programming Languages · Computer Science 2023-12-13 Julia Jansson , Patrik Jansson

Every known communication problem whose randomized communication cost is constant (independent of the input size) can be reduced to $k$-Hamming Distance, that is, solved with a constant number of deterministic queries to some $k$-Hamming…

Computational Complexity · Computer Science 2025-05-07 Yuting Fang , Mika Göös , Nathaniel Harms , Pooya Hatami

In this short note, we initiate the study of the Linear Isomorphism Testing Problem in the setting of communication complexity, a natural linear algebraic generalization of the classical Equality problem. Given Boolean functions $f, g :…

Data Structures and Algorithms · Computer Science 2026-01-13 Swarnalipa Datta , Arijit Ghosh , Chandrima Kayal , Manaswi Paraashar , Manmatha Roy

Quantum mechanics allows operations to be in indefinite causal order. Recently there have been active discussions on enhanced communication strategies through exotic causal structures. In light of this, through the process matrix formalism,…

Quantum Physics · Physics 2021-04-21 Kaumudibikash Goswami , Fabio Costa

Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-11-28 Gianfranco Bilardi , Michele Scquizzato , Francesco Silvestri

In this paper we provide new bounds on classical and quantum distributional communication complexity in the two-party, one-way model of communication. In the classical model, our bound extends the well known upper bound of Kremer, Nisan and…

Information Theory · Computer Science 2008-02-29 Rahul Jain , Shengyu Zhang

Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication…

We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(\log n) qubits for…

Quantum Physics · Physics 2007-05-23 Iordanis Kerenidis , Ran Raz

In this paper we study the separation between the deterministic (classical) query complexity ($D$) and the exact quantum query complexity ($Q_E$) of several Boolean function classes using the parity decision tree method. We first define the…

Quantum Physics · Physics 2020-09-07 Chandra Sekhar Mukherjee , Subhamoy Maitra

Chattopadhyay, Mande and Sherif (ECCC 2018) recently exhibited a total Boolean function, the sink function, that has polynomial approximate rank and polynomial randomized communication complexity. This gives an exponential separation…

Quantum Physics · Physics 2018-11-27 Makrand Sinha , Ronald de Wolf

Suppose we have a two-party communication protocol for $f$ which allows the parties to make queries to an oracle computing $g$; for example, they may query an Equality oracle. To translate this protocol into a randomized protocol, we must…

Computational Complexity · Computer Science 2024-10-15 Nathaniel Harms , Artur Riazanov

We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for…

Quantum Physics · Physics 2008-02-03 Richard Cleve , Wim van Dam , Michael Nielsen , Alain Tapp

The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating a process of state preparation, transmission through the channel and subsequent measurement. It…

Quantum Physics · Physics 2012-09-14 Alberto Montina

The evaluation of a query over a probabilistic database boils down to computing the probability of a suitable Boolean function, the lineage of the query over the database. The method of query compilation approaches the task in two stages:…

Logic in Computer Science · Computer Science 2017-01-18 Simone Bova , Stefan Szeider

Communication is compositional if complex signals can be represented as a combination of simpler subparts. In this paper, we theoretically show that inductive biases on both the training framework and the data are needed to develop a…

Machine Learning · Computer Science 2024-04-04 Łukasz Kuciński , Tomasz Korbak , Paweł Kołodziej , Piotr Miłoś

We consider the problem of communicating over a channel that breaks the message block into fragments of random lengths, shuffles them out of order, and deletes a random fraction of the fragments. Such a channel is motivated by applications…

Information Theory · Computer Science 2024-07-09 Aditya Narayan Ravi , Alireza Vahid , Ilan Shomorony

In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…

Computational Complexity · Computer Science 2010-06-28 Nadia Creignou , Johannes Schmidt , Michael Thomas

Let $R_\epsilon(\cdot)$ stand for the bounded-error randomized query complexity with error $\epsilon > 0$. For any relation $f \subseteq \{0,1\}^n \times S$ and partial Boolean function $g \subseteq \{0,1\}^m \times \{0,1\}$, we show that…

Computational Complexity · Computer Science 2018-11-28 Dmitry Gavinsky , Troy Lee , Miklos Santha , Swagato Sanyal

Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-02-18 Sebastian Siebertz , Alexandre Vigny

For a (possibly partial) Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ as well as a query complexity measure $M$ which maps Boolean functions to real numbers, define the composition limit of $M$ on $f$ by $M^*(f)=\lim_{k\to\infty}…

Computational Complexity · Computer Science 2026-01-14 Bandar Al-Dhalaan , Shalev Ben-David