Related papers: On Probabilistic Checking in Perfect Zero Knowledg…
A recent breakthrough [Hirahara and Nanashima, STOC'2024] established that if $\mathsf{NP} \not \subseteq \mathsf{ioP/poly}$, the existence of zero-knowledge with negligible errors for $\mathsf{NP}$ implies the existence of one-way…
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…
In this paper, motivated by the setting of white-space detection [1], we present theoretical and empirical results for detection of the zero-support E of x \in Cp (xi = 0 for i \in E) with reduced-dimension linear measurements. We propose…
Classical software verification and validation techniques, such as procedural audits, formal methods, or model documentation, are the traditional mechanisms used to achieve the verifiable accountability now required by regulations like the…
Probabilistic circuits (PCs) are a powerful modeling framework for representing tractable probability distributions over combinatorial spaces. In machine learning and probabilistic programming, one is often interested in understanding…
Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such…
Privacy-preserving computation (PPC) methods, such as secure multiparty computation (MPC) and homomorphic encryption (HE), are deployed increasingly often to guarantee data confidentiality in computations over private, distributed data.…
We show that every language in NP has a PCP verifier that tosses $O(\log n)$ random coins, has perfect completeness, and a soundness error of at most $1/\text{poly}(n)$, while making at most $O(\text{poly}\log\log n)$ queries into a proof…
There is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision. Some common forms of prior knowledge include (a) beliefs about which hypotheses are null,…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
Zero-knowledge proofs (ZKPs) are central to secure and privacy-preserving computation, with zk-SNARKs and zk-STARKs emerging as leading frameworks offering distinct trade-offs in efficiency, scalability, and trust assumptions. While their…
We investigate the proof complexity of systems based on positive branching programs, i.e. non-deterministic branching programs (NBPs) where, for any 0-transition between two nodes, there is also a 1-transition. Positive NBPs compute…
Zero-knowledge circuits are sets of equality constraints over arithmetic expressions interpreted in a prime field; they are used to encode computations in cryptographic zero-knowledge proofs. We make the following contributions to the…
The Fewest Clues Problem (FCP) framework has been introduced to study the complexity of determining whether a solution to an \NP~problem can be uniquely identified by specifying a subset of the certificate. For a given problem $P \in \NP$,…
Pre-trained Language Models (PLMs) are trained on large amounts of unlabeled data, yet they exhibit remarkable reasoning skills. However, the trustworthiness challenges posed by these black-box models have become increasingly evident in…
In this paper a proof system is developed for plan verification problems $\{X\}c\{Y\}$ and $\{X\}c\{KW p\}$ under 0-approximation semantics for ${\mathcal A}_K$. Here, for a plan $c$, two sets $X,Y$ of fluent literals, and a literal $p$,…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
Generating code from natural-language requirements has become a primary route for LLM-assisted software development. Although LLMs can successfully complete small programming tasks, generating an entire complex project remains unreliable…
We present a self-contained separation framework for P vs NP developed entirely within ZFC. The approach consists of: (i) a deterministic, radius-1 compilation from uniform polynomial-time Turing computation to local sum-of-squares (SoS)…