Related papers: On the Power of Statistical Zero Knowledge
We address two sets of long-standing open questions in probability theory, from a computational complexity perspective: divisibility of stochastic maps, and divisibility and decomposability of probability distributions. We prove that finite…
We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms…
The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the…
Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two…
A zero-knowledge proximity proof certifies geometric nearness but carries no commitment to an application context. In stateful geo-content systems, where drops can share coordinates, policies evolve, and content has persistent identity,…
Zero-Shot Learning (ZSL) presents the challenge of identifying categories not seen during training. This task is crucial in domains where it is costly, prohibited, or simply not feasible to collect training data. ZSL depends on a mapping…
We consider a committee voting setting in which each voter approves of a subset of candidates and based on the approvals, a target number of candidates are selected. Aziz et al. (2015) proposed two representation axioms called justified…
Elliptic Curve Cryptography (ECC) is an attractive alternative to conventional public key cryptography, such as RSA. ECC is an ideal candidate for implementation on constrained devices where the major computational resources i.e. speed,…
Zero-shot coordination (ZSC) is a popular setting for studying the ability of reinforcement learning (RL) agents to coordinate with novel partners. Prior ZSC formulations assume the $\textit{problem setting}$ is common knowledge: each agent…
Zero-Shot Learning (ZSL) aims to recognize unseen classes by generalizing the knowledge, i.e., visual and semantic relationships, obtained from seen classes, where image augmentation techniques are commonly applied to improve the…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…
A strong direct product theorem states that, in order to solve k instances of a problem, if we provide less than k times the resource required to compute one instance, then the probability of overall success is exponentially small in k. In…
We build on a working program initiated by Pudl\'ak [Pud17] and construct an oracle relative to which each $\mathrm{coNP}$-complete set has $\mathrm{P}$-optimal proof systems and $\mathrm{NP}\cap\mathrm{coNP}$ does not have complete…
We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable…
Formal reasoning about the time complexity of algorithms and data structures is usually done in interactive theorem provers like Isabelle/HOL. This includes reasoning about amortized time complexity which looks at the worst case performance…
Survey propagation (SP) is an exciting new technique that has been remarkably successful at solving very large hard combinatorial problems, such as determining the satisfiability of Boolean formulas. In a promising attempt at understanding…
We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…
The constraint satisfaction problem (CSP) can be formulated as a homomorphism problem between relational structures: given a structure $\mathcal{A}$, for any structure $\mathcal{X}$, whether there exists a homomorphism from $\mathcal{X}$ to…