Related papers: Geometric Theory for Program Testing
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
Vision systems, i.e., systems that allow to detect and track objects in images, have gained substantial importance over the past decades. They are used in quality assurance applications, e.g., for finding surface defects in products during…
In many situations it could be interesting to ascertain whether nonparametric regression curves can be grouped, especially when confronted with a considerable number of curves. The proposed testing procedure allows to determine groups with…
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
There are countless reasons cited in scientific studies to explain the difficulties in programming learning. The reasons range from the subject's complexity, the ineffective teaching and study methods, to psychological aspects such as…
The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects.…
This paper shows that a variety of software model-checking algorithms can be seen as proof-search strategies for a non-standard proof system, known as a cyclic proof system. Our use of the cyclic proof system as a logical foundation of…
We present a geometric proof for the duality theorem of linear programming. Besides being self-contained and simple, the present approach also provides a transparent way for understanding this fundamental result.
The test pyramid is a conceptual model that describes how quality checks can be organized to ensure coverage of all components of a system, at all scales. Originally conceived to help aerospace engineers plan tests to determine how material…
In this paper we study possibilities of using hierarchical reasoning, symbol elimination and model generation for the verification of parametric systems, where the parameters can be constants or functions. Our goal is to automatically…
Can one estimate the number of remaining faults in a software system? A credible estimation technique would be immensely useful to project managers as well as customers. It would also be of theoretical interest, as a general law of software…
Even competent programmers make mistakes. Automatic verification can detect errors, but leaves the frustrating task of finding the erroneous line of code to the user. This paper presents an automatic approach for identifying potential error…
As the computer vision matures into a systems science and engineering discipline, there is a trend in leveraging latest advances in computer graphics simulations for performance evaluation, learning, and inference. However, there is an open…
We introduce and discuss, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true and false over some relevant collections of instances. A rigorous, algorithmic…
These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we…
Formal verification provides mathematical guarantees that a software is correct. Design-level verification tools ensure software specifications are correct, but they do not expose defects in actual implementations. For this purpose,…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…