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This paper is about solving polynomial systems. It first recalls how to do that efficiently with a very high probability of correctness by reconstructing a rational univariate representation (rur) using Groebner revlex computation,…
This work addresses the correct translation of an Event-B model to C code via an intermediate formal language, HLL. The proof of correctness follows two main steps. First, the final refinement of the Event-B model, including invariants, is…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
Stream Runtime Verification is a formal dynamic analysis technique that generalizes runtime verification algorithms from temporal logics like LTL to stream monitoring, allowing to compute richer verdicts than Booleans (including…
Transformer-based Large Language Models (LLMs) have demonstrated powerful in-context learning capabilities. However, their predictions can be disrupted by factually correct context, a phenomenon known as context hijacking, revealing a…
In this paper, we give algorithms for determining the existence of isomorphism between two finite-dimensional Lie algebras and compute such an isomorphism in the affirrmative case. We also provide algorithms for determining algebraic…
In this paper we consider the problem of certified static checking of module-like constructs of programming languages. We argue that there are algorithms and properties related to modules that can be defined and proven in an abstract way.…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
Machine-translated text plays an important role in modern life by smoothing communication from various communities using different languages. However, unnatural translation may lead to misunderstanding, a detector is thus needed to avoid…
This paper presents an efficient adaptation and application of the Dempster-Shafer theory of evidence, one that can be used effectively in a massively parallel hierarchical system for visual pattern perception. It describes the techniques…
Based on our previous work on algebraic laws for true concurrency, we design a structured parallel programming language for true concurrency called PPL. Different to most programming languages, PPL has an explicit parallel operator as an…
A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts…
Rhetoric, both spoken and written, involves not only content but also style. One common stylistic tool is $\textit{parallelism}$: the juxtaposition of phrases which have the same sequence of linguistic ($\textit{e.g.}$, phonological,…
The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint…
Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the…
This paper presents an effective approach for parallel corpus mining using bilingual sentence embeddings. Our embedding models are trained to produce similar representations exclusively for bilingual sentence pairs that are translations of…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
Linearizability is the standard correctness criterion concurrent data structures such as stacks and queues. It allows to establish observational refinement between a concurrent implementation and an atomic reference implementation.Proving…
One of the main challenges in distributed computing is building interfaces and APIs that allow programmers with limited background in distributed systems to write scalable, performant, and fault-tolerant applications on large clusters. In…
Refinement Reflection turns your favorite programming language into a proof assistant by reflecting the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses of the function, the…