Related papers: Certifying floating-point implementations using Ga…

Software testing uses wide range of different tools to enhance the complicated process of defining quality of the system under test. Formal Concept Analysis (FCA) provides us with algorithms of deriving formal ontology from a set of objects…

Large language models have become increasingly effective in software engineering tasks such as code generation, debugging and repair. Language models like ChatGPT can not only generate code, but also explain its inner workings and in…

Floating-point arithmetic plays a central role in science, engineering, and finance by enabling developers to approximate real arithmetic. To address numerical issues in large floating-point applications, developers must identify root…

Applying deductive verification to formally prove that a program respects its formal specification is a very complex and time-consuming task due in particular to the lack of feedback in case of proof failures. Along with a non-compliance…

Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…

Interval arithmetic libraries provide the four elementary arithmetic operators for operand intervals bounded by floating-point numbers. Actual implementations need to make a large case analysis that considers, e.g., magnitude relations…

We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…

For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…

Floating-point programs form the foundation of modern science and engineering, providing the essential computational framework for a wide range of applications, such as safety-critical systems, aerospace engineering, and financial analysis.…

This tutorial provides an introduction to CPAchecker for users. CPAchecker is a flexible and configurable framework for software verification and testing. The framework provides many abstract domains, such as BDDs, explicit values,…

Cyber-physical systems, such as learning robots and other autonomous systems, employ high-integrity software in their safety-critical control. This software is developed using a range of tools some of which need to be qualified for this…

Floating-point accuracy is an important concern when developing numerical simulations or other compute-intensive codes. Tracking the introduction of numerical regression is often delayed until it provokes unexpected bug for the end-user. In…

Probabilistic pushdown automata (pPDA) are a standard model for discrete probabilistic programs with procedures and recursion. In pPDA, many quantitative properties are characterized as least fixpoints of polynomial equation systems. In…

This article describes a prototype implementation of a web interface for the Matita proof assistant. The interface supports all basic functionalities of the local Gtk interface, but takes advantage of the markup to enrich the document with…

In introductory programming courses, it is challenging for instructors to provide debugging feedback on students' incorrect programs. Some recent tools automatically offer program repair feedback by identifying any differences between…

From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…

Gradual verification soundly combines static checking and dynamic checking to provide an incremental approach for software verification. With gradual verification, programs can be partially specified first, and then the full specification…

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…

There is a growing interest in the use of reduced-precision arithmetic, exacerbated by the recent interest in artificial intelligence, especially with deep learning. Most architectures already provide reduced-precision capabilities (e.g.,…

Modern programmable digital signal processing relies on floating-point numbers for their ease of use. Fixed-point number formats have the potential to save resources and improve execution time, but realising this potential burdens the…