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Formal verification of floating-point arithmetic remains challenging due to non-linear arithmetic behavior and the tight coupling between control and datapath logic. Existing approaches often rely on high-level C models for equivalence…
We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our…
In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…
Weighted model counting computes the sum of the rational-valued weights associated with the satisfying assignments for a Boolean formula, where the weight of an assignment is given by the product of the weights assigned to the positive and…
Interval arithmetic is hardly feasible without directed rounding as provided, for example, by the IEEE floating-point standard. Equally essential for interval methods is directed rounding for conversion between the external decimal and…
This study addresses the critical issue of factual inaccuracies in machine-generated text summaries, an increasingly prevalent issue in information dissemination. Recognizing the potential of such errors to compromise information…
In this paper, a monad-based denotational model is introduced and shown adequate for the Proto-Quipper family of calculi, themselves being idealized versions of the Quipper programming language. The use of a monadic approach allows us to…
We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
The coordinate rotation digital computer (CORDIC) is a shift-add based fast computing algorithm which has been found in many digital signal processing (DSP) applications. In this paper, a detailed error analysis based on mean square error…
Randomized rounding is a standard method, based on the probabilistic method, for designing combinatorial approximation algorithms. In Raghavan's seminal paper introducing the method (1988), he writes: "The time taken to solve the linear…
This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…
Recent studies have pointed out that natural language processing (NLP) models are vulnerable to backdoor attacks. A backdoored model produces normal outputs on the clean samples while performing improperly on the texts with triggers that…
We extend intersection types to a computational $\lambda$-calculus with algebraic operations \`a la Plotkin and Power. We achieve this by considering monadic intersections, whereby computational effects appear not only in the operational…
The rapid advancement of large language models (LLMs) has significantly improved code completion tasks, yet the trade-off between accuracy and computational cost remains a critical challenge. While using larger models and incorporating…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens…
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational…
Word embedding is an essential building block for deep learning methods for natural language processing. Although word embedding has been extensively studied over the years, the problem of how to effectively embed numerals, a special subset…
Large language models (LLMs) can solve an increasing number of complex reasoning tasks while making surprising mistakes in basic numerical understanding and processing (such as 9.11 > 9.9). The latter ability is essential for tackling…