相关论文: A Tight Parallel Repetition Theorem for Partially …

In this work, we show that parallel repetition of public-coin interactive arguments reduces the soundness error at an exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers,…

In this note, we show that $O(\log (1/\epsilon))$ rounds of parallel repetition with a threshold suffice to reduce completeness and soundness error to $\epsilon$ for single-prover quantum interactive proof systems. This improves on a…

The class $\MIP^*$ of promise problems that can be decided through an interactive proof system with multiple entangled provers provides a complexity-theoretic framework for the exploration of the nonlocal properties of entanglement. Little…

We prove a tight parallel repetition theorem for $3$-message computationally-secure quantum interactive protocols between an efficient challenger and an efficient adversary. We also prove under plausible assumptions that the security of…

In this thesis, we answer several questions about the behaviour of prover-verifier interactions under parallel repetition when quantum information is allowed, and the verifier acts independently in them. We first consider the case in which…

We generalize the feasible interpolation theorem for semantic derivations from K.(1997) by allowing randomized protocols (protocols in the sense of K.(1997). We also introduce an extension of the monotone circuit model, monotone circuits…

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…

A central problem in quantum computational complexity is how to prevent entanglement-assisted cheating in multi-prover interactive proof systems. It is well-known that the standard oracularization technique completely fails in some proof…

This is the full version of a paper submitted to the Computability in Europe (CiE 2023) conference, with all proofs omitted there. In 2012 P. D. Azar and S. Micali introduced a new model of interactive proofs, called "Rational Interactive…

The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…

We present a generic compiler that converts any $\mathsf{MIP}^{*}$ protocol into a succinct interactive argument where the communication and the verifier are classical, and where post-quantum soundness relies on the post-quantum…

Quantum effect enables enhanced estimation precision in metrology, with the Heisenberg limit (HL) representing the ultimate limit allowed by quantum mechanics. Although the HL is generally unattainable in the presence of noise, quantum…

Random selection, leader election, and collective coin flipping are fundamental tasks in fault-tolerant distributed computing. We study these problems in the full-information model where despite decades of study, key gaps remain in our…

A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return is allowed to err with some bounded probability. The…

The pursuit of a "unified" discrete token for both speech understanding and generation has led the Speech Language Model (SLM) community to heavily rely on Word Error Rate (WER) -- the core metric for Whisper-style tokenizers -- as the…

Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…

We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasiprobability…

We present $\textbf{P}$robabilistically $\textbf{T}$ightened $\textbf{Li}$near $\textbf{R}$elaxation-based $\textbf{P}$erturbation $\textbf{A}$nalysis ($\texttt{PT-LiRPA}$), a novel framework that combines over-approximation techniques from…

Scaling inference-time computation has substantially improved the reasoning capabilities of language models. However, existing methods have significant limitations: serialized chain-of-thought approaches generate overly long outputs,…

Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM…