Related papers: Algebraic Principles for Rely-Guarantee Style Conc…
This is an overview of the Isabelle technology behind the Archive of Formal Proofs (AFP). Interactive development and quasi-interactive build jobs impose significant demands of scalability on the logic (usually Isabelle/HOL), on Isabelle/ML…
Formal verification (FV) has witnessed growing significance with current emerging program synthesis by the evolving large language models (LLMs). However, current formal verification mainly resorts to symbolic verifiers or hand-craft rules,…
Obtaining enough labeled data to robustly train complex discriminative models is a major bottleneck in the machine learning pipeline. A popular solution is combining multiple sources of weak supervision using generative models. The…
A method for the analytical evaluation of layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for piecewise flat boundary elements with polynomial shape functions. The…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
We present a complete polymorphic effect inference algorithm for an ML-style language with handlers of not only exceptions, but of any other algebraic effect such as input & output, mutable references and many others. Our main aim is to…
Reactive programs combine traditional sequential programming constructs with primitives to allow communication with other concurrent agents. They are ubiquitous in modern applications, ranging from components systems and web services, to…
We propose and investigate probabilistic guarantees for the adversarial robustness of classification algorithms. While traditional formal verification approaches for robustness are intractable and sampling-based approaches do not provide…
Purpose: This study extends the structural theory of finite commutative ternary $\Gamma$-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration…
We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics…
Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic…
Machine learning models are generally vulnerable to adversarial examples, which is in contrast to the robustness of humans. In this paper, we try to leverage one of the mechanisms in human recognition and propose a bio-inspired…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
An event structure is a mathematical abstraction modeling concepts as causality, conflict and concurrency between events. While many other mathematical structures, including groups, topological spaces, rings, abound with algorithms and…
Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we…
We present a complete formalization in Isabelle/HOL of the object part of an equivalence between L-mosaics and bounded join-semilattices, employing an AI-assisted methodology that integrates large language models as reasoning assistants…
There are several ways to define program equivalence for functional programs with algebraic effects. We consider two complementing ways to specify behavioural equivalence. One way is to specify a set of axiomatic equations, and allow proof…
Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by having models self-verify each response for correctness. In this paper, we…
Scaling inference compute in large language models (LLMs) through repeated sampling consistently increases the coverage (fraction of problems solved) as the number of samples increases. We conjecture that this observed improvement is…
The foundations of formal models for epistemic and doxastic logics often rely on certain logical aspects of modal logics such as S4 and S4.2 and their semantics; however, the corresponding mathematical results are often stated in papers or…