Related papers: Query-to-Communication Lifting for BPP
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…
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…
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 $f, g :…
Quantum mechanics allows operations to be in indefinite causal order. Recently there have been active discussions on enhanced communication strategies through exotic causal structures. In light of this, through the process matrix formalism,…
Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower…
In this paper we provide new bounds on classical and quantum distributional communication complexity in the two-party, one-way model of communication. In the classical model, our bound extends the well known upper bound of Kremer, Nisan and…
Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication…
We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(\log n) qubits for…
In this paper we study the separation between the deterministic (classical) query complexity ($D$) and the exact quantum query complexity ($Q_E$) of several Boolean function classes using the parity decision tree method. We first define the…
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…
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…
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…
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…
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:…
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…
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…
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.…
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…
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…
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}…