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The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter…
Resilience is one of the key algorithmic problems underlying various forms of reverse data management (such as view maintenance, deletion propagation, and various interventions for fairness): What is the minimal number of tuples to delete…
Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These…
A plethora of jailbreaking attacks have been proposed to obtain harmful responses from safety-tuned LLMs. These methods largely succeed in coercing the target output in their original settings, but their attacks vary substantially in…
A dictionary data structure maintains a set of at most $n$ keys from the universe $[U]$ under key insertions and deletions, such that given a query $x \in [U]$, it returns if $x$ is in the set. Some variants also store values associated to…
The study of hashing is closely related to the analysis of balls and bins. It is well-known that instead of using a single hash function if we randomly hash a ball into two bins and place it in the smaller of the two, then this dramatically…
The iterative conditional branchings appear in various sensitive algorithms, like the modular exponentiation in the RSA cryptosystem or the scalar multiplication in ellipticcurve cryptography. In this paper, we abstract away the desirable…
The existence of quantum uncertainty relations is the essential reason that some classically impossible cryptographic primitives become possible when quantum communication is allowed. One direct operational manifestation of these…
In using the Bayesian network (BN) to construct the complex multistate system's reliability model as described in Part I, the memory storage requirements of the node probability table (NPT) will exceed the random access memory (RAM) of the…
Replicability requires that algorithmic conclusions remain consistent when rerun on independently drawn data. A central structural question is composition: given $k$ problems each admitting a $\rho$-replicable algorithm with sample…
Testing the equality of two high-dimensional mean vectors is a fundamental problem in multivariate analysis. While the classical Hotelling's $T^2$ test is optimal in low-dimensional settings, it fails when the dimension $p$ is comparable to…
We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…
The success of neural networks in image classification has inspired various hardware implementations on embedded platforms such as Field Programmable Gate Arrays, embedded processors and Graphical Processing Units. These embedded platforms…
Locally Decodable Codes (LDCs) are error-correcting codes $C:\Sigma^n\rightarrow \Sigma^m$ with super-fast decoding algorithms. They are important mathematical objects in many areas of theoretical computer science, yet the best…
The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could…
Memory reclamation for lock-based data structures is typically easy. However, it is a significant challenge for lock-free data structures. Automatic techniques such as garbage collection are inefficient or use locks, and non-automatic…
We propose a conceptually simple oblivious sort and oblivious random permutation algorithms called bucket oblivious sort and bucket oblivious random permutation. Bucket oblivious sort uses $6n\log n$ time (measured by the number of memory…
We introduce a simple method for probabilistic predictions on tabular data based on Large Language Models (LLMs) called JoLT (Joint LLM Process for Tabular data). JoLT uses the in-context learning capabilities of LLMs to define joint…
We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…
Large Language Models (LLMs) can enhance analytics systems with powerful data summarization, cleaning, and semantic transformation capabilities. However, deploying LLMs at scale -- processing millions to billions of rows -- remains…