Related papers: Formally Verified Argument Reduction with a Fused-…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
We consider the problem of accurate computation of the finite difference $f(\x+\s)-f(\x)$ when $\Vert\s\Vert$ is very small. Direct evaluation of this difference in floating point arithmetic succumbs to cancellation error and yields 0 when…
Through the advent of pre-trained language models, there have been notable advancements in abstractive summarization systems. Simultaneously, a considerable number of novel methods for evaluating factual consistency in abstractive…
Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently…
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…
Acceleration in symbolic verification consists in computing the exact effect of some control-flow loops in order to speed up the iterative fix-point computation of reachable states. Even if no termination guarantee is provided in theory,…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
While LLM-based agents are able to tackle a wide variety of code reasoning questions, the answers are not always correct. This prevents the agent from being useful in situations where high precision is desired: (1) helping a software…
With the increasing availability of parallel computing power, there is a growing focus on parallelizing algorithms for important automated reasoning problems such as Boolean satisfiability (SAT). Divide-and-Conquer (D&C) is a popular…
Self-Consistency samples diverse reasoning chains with answers and chooses the final answer by majority voting. It is based on forward reasoning and cannot further improve performance by sampling more reasoning chains when saturated. To…
Verification of numerical accuracy properties in modern software remains an important and challenging task. This paper describes an original framework combining different solutions for numerical accuracy. First, we extend an existing…
Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not…
Self-consistency-based approaches, which involve repeatedly sampling multiple outputs and selecting the most consistent one as the final response, prove to be remarkably effective in improving the factual accuracy of large language models.…
We extract verified algorithms for exact real number computation from constructive proofs. To this end we use a coinductive representation of reals as streams of binary signed digits. The main objective of this paper is the formalisation of…
Fact-checking real-world claims often requires collecting multiple pieces of evidence and applying complex multi-step reasoning. In this paper, we present Program-Guided Fact-Checking (ProgramFC), a novel fact-checking model that decomposes…
Automated fact-checking based on machine learning is a promising approach to identify false information distributed on the web. In order to achieve satisfactory performance, machine learning methods require a large corpus with reliable…
Formal verification techniques are widely used for detecting design flaws in software systems. Formal verification can be done by transforming an already implemented source code to a formal model and attempting to prove certain properties…
The key limitation of the verification performance lies in the ability of error detection. With this intuition we designed several variants of pessimistic verification, which are simple workflows that could significantly improve the…