Danny Harnik, Moni Naor

We initiate the study of the compressibility of NP problems. We

consider NP problems that have long instances but relatively

short witnesses. The question is, can one efficiently compress an

instance and store a shorter representation that maintains the

information of whether the original input is in the language or

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David Doty

A dimension extractor is an algorithm designed to increase the effective dimension -- i.e., the computational information density -- of an infinite sequence. A constructive dimension extractor is exhibited by showing that every sequence of positive constructive dimension is Turing equivalent to a sequence of constructive strong dimension arbitrarily ... more >>>

Scott Aaronson, Andrew Drucker

We prove the following surprising result: given any quantum state rho on n qubits, there exists a local Hamiltonian H on poly(n) qubits (e.g., a sum of two-qubit interactions), such that any ground state of H can be used to simulate rho on all quantum circuits of fixed polynomial size. ... more >>>

Mark Braverman, Anup Rao

We show how to efficiently simulate the sending of a message M to a receiver who has partial information about the message, so that the expected number of bits communicated in the simulation is close to the amount of additional information that the message reveals to the receiver.

We ... more >>>

Marius Zimand

We show that if DTIME[2^{O(n)}] is not included in DSPACE}[2^{o(n)}], then, for every set B in PSPACE, all strings x in B of length n can be represented by a string compressed(x) of length at most log (|B^{=n}|) + O(log n), such that a polynomial-time algorithm, given compressed(x), can distinguish ... more >>>

Valentine Kabanets, Antonina Kolokolova

We consider the problem of compression for ``easy'' Boolean functions: given the truth table of an $n$-variate Boolean function $f$ computable by some \emph{unknown small circuit} from a \emph{known class} of circuits, find in deterministic time $\poly(2^n)$ a circuit $C$ (no restriction on the type of $C$) computing $f$ so ... more >>>

Balthazar Bauer, Shay Moran, Amir Yehudayoff

We study internal compression of communication protocols

to their internal entropy, which is the entropy of the transcript from the players' perspective.

We first show that errorless compression to the internal entropy

(and hence to the internal information) is impossible.

We then provide two internal compression schemes with error.

One ...
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Anat Ganor, Gillat Kol, Ran Raz

We show an exponential gap between communication complexity and information complexity for boolean functions, by giving an explicit example of a partial function with information complexity $\leq O(k)$, and distributional communication complexity $\geq 2^k$. This shows that a communication protocol for a partial boolean function cannot always be compressed to ... more >>>

Venkatesan Guruswami, Ameya Velingker

We prove a lower estimate on the increase in entropy when two copies of a conditional random variable $X | Y$, with $X$ supported on $\mathbb{Z}_q=\{0,1,\dots,q-1\}$ for prime $q$, are summed modulo $q$. Specifically, given two i.i.d. copies $(X_1,Y_1)$ and $(X_2,Y_2)$ of a pair of random variables $(X,Y)$, with $X$ ... more >>>

Igor Carboni Oliveira, Rahul Santhanam

We consider $\cal C$-compression games, a hybrid model between computational and communication complexity. A $\cal C$-compression game for a function $f \colon \{0,1\}^n \to \{0,1\}$ is a two-party communication game, where the first party Alice knows the entire input $x$ but is restricted to use strategies computed by $\cal C$-circuits, ... more >>>

Benny Applebaum, Sergei Artemenko, Ronen Shaltiel, Guang Yang

A circuit $C$ \emph{compresses} a function $f:\{0,1\}^n\rightarrow \{0,1\}^m$ if given an input $x\in \{0,1\}^n$ the circuit $C$ can shrink $x$ to a shorter $\ell$-bit string $x'$ such that later, a computationally-unbounded solver $D$ will be able to compute $f(x)$ based on $x'$. In this paper we study the existence of ... more >>>

Anat Ganor, Gillat Kol, Ran Raz

We show an exponential gap between communication complexity and external information complexity, by analyzing a communication task suggested as a candidate by Braverman [Bra13]. Previously, only a separation of communication complexity and internal information complexity was known [GKR14,GKR15].

More precisely, we obtain an explicit example of a search problem with ... more >>>

Yael Tauman Kalai, Ilan Komargodski

We show how to compress communication in distributed protocols in which parties do not have private inputs. More specifically, we present a generic method for converting any protocol in which parties do not have private inputs, into another protocol where each message is "short" while preserving the same number of ... more >>>

Marshall Ball, Elette Boyle, Akshay Degwekar, Apoorvaa Deshpande, Alon Rosen, Vinod Vaikuntanathan, Prashant Vasudevan

Reductions between problems, the mainstay of theoretical computer science, efficiently map an instance of one problem to an instance of another in such a way that solving the latter allows solving the former. The subject of this work is ``lossy'' reductions, where the reduction loses some information about the input ... more >>>

Zhenjian Lu, Igor Carboni Oliveira

A probabilistic representation of a string $x \in \{0,1\}^n$ is given by the code of a randomized algorithm that outputs $x$ with high probability [Oliveira, ICALP 2019]. We employ probabilistic representations to establish the first unconditional Coding Theorem in time-bounded Kolmogorov complexity. More precisely, we show that if a distribution ... more >>>