Related papers: Geometric Theory for Program Testing
Formal software verification uses mathematical techniques to establish that software has certain properties. For example, that the behaviour of a software system satisfies certain logically-specified properties. Formal methods have a long…
With the advent of WWW and outburst in technology and software development, testing the software became a major concern. Due to the importance of the testing phase in a software development life cycle, testing has been divided into…
Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…
We define a Graphics Turing Test to measure graphics performance in a similar manner to the definition of the traditional Turing Test. To pass the test one needs to reach a computational scale, the Graphics Turing Scale, for which Computer…
Systematic testing of object-oriented software turned out to be much more complex than testing conventional software. Especially the highly incremental and iterative development cycle demands both many more changes and partially implemented…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
Software measurement programs have emerged as compounds of several measurement activities that are pursued as part of a combined effort of several parties within a software organization, based on interests that the organization has…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
Topological data analysis involves the statistical characterization of the shape of data. Persistent homology is a primary tool of topological data analysis, which can be used to analyze topological features and perform statistical…
Neural networks are increasingly applied to support decision making in safety-critical applications (like autonomous cars, unmanned aerial vehicles and face recognition based authentication). While many impressive static verification…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
A program verifier is a tool that can be used to verify that a "contract" for a program holds - i.e. given a precondition the program guarantees that a given postcondition holds - by only working at the level of the annotated program. An…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
There are two ways to check if a program is correct, namely execute it or review it. While executing a program is the ultimate test for its correctness reviewing the program can occur earlier in its development and find problems if done…
In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical…
Embedded systems are ubiquitous and play critical roles in management systems for industry and transport. Software failures in these domains may lead to loss of production or even loss of life, so the software in these systems needs to be…
We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of…
A fully geometric procedure of quantization that utilizes a natural and necessary metric on phase space is reviewed and briefly related to the goals of the program of geometric quantization.
Deep neural networks have been increasingly used in software engineering and program analysis tasks. They usually take a program and make some predictions about it, e.g., bug prediction. We call these models neural program analyzers. The…
Among the components contributing to particle transport, geometry navigation is an important consumer of CPU cycles. The tasks performed to get answers to "basic" queries such as locating a point within a geometry hierarchy or computing…