Kol and Raz [STOC 2013] showed how to simulate any alternating two-party communication protocol designed to work over the noiseless channel, by a protocol that works over a stochastic channel that corrupts each sent symbol with probability ‍є>0 ...

Quantum entanglement is a fundamental property of quantum mechanics and it serves as a basic resource in quantum computation and information. Despite its importance, the power and limitations of quantum entanglement are far from being fully ...

Given a graph and an integer k, Densest k-Subgraph is the algorithmic task of finding the subgraph on k vertices with the maximum number of edges. This is a fundamental problem that has been subject to intense study for decades, with applications ...

We prove that the Minimum Distance Problem (MDP) on linear codes over any fixed finite field and parameterized by the input distance bound is W[1]-hard to approximate within any constant factor. We also prove analogous results for the parameterized ...

The complexity of free games with two or more classical players was essentially settled by Aaronson, Impagliazzo, and Moshkovitz (CCC’14). In the quantum world, there are two complexity classes that can be considered quantum analogues of classical ...

Strong (resp. weak) average-case hardness refers to the properties of a computational problem in which a large (resp. small) fraction of instances are hard to solve. We develop a general framework for proving hardness self-amplification, that is, the ...

We show how to obfuscate pseudo-deterministic quantum circuits, assuming the quantum hardness of learning with errors (QLWE) and post-quantum virtual black-box (VBB) obfuscation for classical circuits. Given the classical description of a quantum ...

A (single server) private information retrieval (PIR) allows a client to read data from a public database held on a remote server, without revealing to the server which locations she is reading. In a doubly efficient PIR (DEPIR), the database is first ...

We show a general method of compiling any k-prover non-local game into a single-prover (computationally sound) interactive game maintaining the same quantum completeness and classical soundness guarantees, up to a negligible additive factor in a ...

We develop a new technique for analyzing linear independence of multivariate polynomials. One of our main technical contributions is a Small Witness for Linear Independence (SWLI) lemma which states the following. If the polynomials f₁,f₂, …, f_k ∈ F[X]...

Symmetry of Information (SoI) is a fundamental property of Kolmogorov complexity that relates the complexity of a pair of strings and their conditional complexities. Understanding if this property holds in the time-bounded setting is a longstanding open ...

A Chor–Goldreich (CG) source is a sequence of random variables X = X₁ ∘ … ∘ X_t, where each X_i ∼ {0,1}^d and X_i has δ d min-entropy conditioned on any fixing of X₁ ∘ … ∘ X_i−1. The parameter 0<δ≤ 1 is the entropy rate of the source. We typically think of ...

In a work by Raz (J. ACM and FOCS 16), it was proved that any algorithm for parity learning on n bits requires either Ω(n²) bits of classical memory or an exponential number (in ‍n) of random samples. A line of recent works continued that research ...

In the setting of error-correcting codes with feedback, Alice wishes to communicate a k-bit message x to Bob by sending a sequence of bits over a channel while noiselessly receiving feedback from Bob. It has been long known (Berlekamp, 1964) that in ...

The existence of “unstructured” hard languages in NP  ∩ coNP is an intriguing open question. Bennett and Gill (SICOMP, 1981) asked whether P is separated from NP ∩ coNP relative to a random oracle, a question that remained open ever since. While a ...

We prove the first unconditional consistency result for superpolynomial circuit lower bounds with a relatively strong theory of bounded arithmetic. Namely, we show that the theory ‍V₂⁰ is consistent with the conjecture that ‍NEXP ‍⊈ ‍P/poly, i.e., ...

We study the following question: what cryptographic assumptions are needed for obtaining constant-round computationally-sound argument systems? We focus on argument systems with almost-linear verification time for subclasses of P, such as depth-...

The “short cycle removal” technique was recently introduced by Abboud, Bringmann, Khoury and Zamir (STOC ’22) to prove fine-grained hardness of approximation. Its main technical result is that listing all triangles in an n^1/2-regular graph is n^2−o(1)-...

The δ-Coin Problem is the problem of distinguishing between a sequence of coin tosses that come up Heads with probability either 1+δ/2 or 1−δ/2. The computational complexity of this problem in various models has been studied in many previous works ...

We give a polynomial time classical algorithm for sampling from the output distribution of a noisy random quantum circuit in the regime of anti-concentration to within inverse polynomial total variation distance. The algorithm is based on a quantum ...