Software testing is an important part of the software development process but typically is manual, expensive, and error prone. This has led to significant interest in automated test generation (and execution) algorithms, with these having the potential to lead to cheaper, higher-quality software. Despite the interest in automating parts of testing, there are still significant challenges, with auto-testing being mentioned as an EPSRC priority within Software Engineering. This project will build on initial work by the PIs that has demonstrated that an important aspect of testing can be represented in terms of Quantified Information Flow. Specifically, the PIs previously looked at Failed Error Propagation (FEP), which is sometimes called coincidental correctness. In FEP, a test execution goes through a faulty part of the software, this leads to what would be regarded as a corrupted program state (i.e. the fault has an effect) but ultimately the output is correct. Although studies have shown that FEP can significantly reduce test effectiveness, there is a lack of practical techniques that address FEP. The observation made by the PIs is that FEP corresponds to a failure for information to flow from the fault in the software to output: information is lost through different values for the program state (correct and faulty values) being mapped to the same output. The PIs have shown how FEP can be represented in terms of an information theoretic notion: Quantified Information Flow (QIF). The results of experiments were highly promising, with there being a rank correlation of over 0.95 between the frequency with which FEP was observed in software and a QIF-based metric. This remarkably strong result opens up the possibility of devising techniques that generate test cases that are less likely to suffer from FEP. In addition, we believe that it is possible to represent other important testing concepts using information theory, specifically: the 'feasibility' of a path (we do not want test automation to waste effort in trying to trigger infeasible paths), the diversity of a test suite (evidence suggests that diverse test suites are effective), and also the effectiveness of probes/oracles added to the code. This project will develop new methods, based on information theory, for reasoning about the above factors (FEP, feasibility, diversity, and oracles). In doing so it will develop information theoretic measures that can help test automation to overcome the associated issues. It will also develop methods for estimating these measures, integrate these estimates into automated test generation, and evaluate the results on open source software and software provided by our industrial partners. The outcome will be a new theory for software testing, based on information theory, and a set of techniques that use this theory to make software testing more efficient and effective.

Progress in sensing, computational power, storage and analytic tools has given us access to enormous amounts of complex data, which can inform us of better ways to manage our cities, run our companies or develop new medicines. However, the 'elephant in the room' is that when we act on that data we change the world, potentially invalidating the older data. Similarly, when monitoring living cities or companies, we are not able to run clean experiments on them - we get data which is affected by the way they are run today, which limits our ability to model these complex systems. We need ways to run ongoing experiments on such complex systems. We also need to support human interactions with large and complex data sets. In this project we will look at the overlap between the challenge someone faces when coping with all the choices associated with booking a flight for a weekend away, and an expert running complex experiments in a laboratory. The project will test the core ideas in a number of areas, including personalisation of hearing aids, analysis of cancer data, and adapting the computing resources for a major bank.

Advanced digital systems provide many exciting opportunities for UK economic growth. Our current Platform Grant has enabled us to implement a strategy of developing novel custom computing solutions, which involve customising the latest hardware and software elements, to meet demanding requirements from many applications. These include embedded systems applications such as software-defined radio and patient monitoring, as well as high-performance computing applications such as financial modelling and medical imaging. Continued Platform Grant funding will allow us to build on our success, to support strategic development of our team, and to extend our lead in custom computing technology to cover a wide variety of advanced digital systems for healthcare, environment, and security applications.There are three new strategic directions on which we are uniquely capable of making major impacts. We plan to conduct exploratory research to identify promising projects for responsive-mode funding for the following:1. customisable heterogeneous architectures, including design space exploration of devices and systems, relevant development methods and tools, and prototyping platforms and design portability enhancement;2. self-adapting design, including architecture innovations, adaptation policies and optimisation strategies, and design and verification flow;3. security-aware systems, including architecture enhancements, compilation and test generation environments, and experimental facilities and demonstration flow.The added value aspects for this Platform Grant proposal include: (a) providing continuity of support, (b) exploring significant strategic directions, (c) contributing to research infra-structure, (d) attracting fresh talents, (e) pioneering and strengthening international collaborations, and (f) accelerating technology transfer.

Since the advent of numerical weather prediction in the early twentieth century, physics driven computational modelling has gone from strength to strength, underpinning much of the modern world, from the design of new bridges and buildings that can withstand earthquakes, to the aerodynamic optimisation of airplanes and the simulation of materials for batteries underpinning the electric car revolution. But physics based models alone have limits in what they can do. From high dimensional control problems to multiscale fluid flow, there are many important systems where conventional discretise-and-solve approaches remain permanently out reach. In other important systems, we have no physical models at all (in natural language processing and many other areas). In these data based approaches we have seen tremendous advances over the last decade, exemplified by the deep learning revolution. There is a now a growing consensus that computational models of tomorrow will consist of combinations of physics and data driven approaches and should not be viewed separately from each other. There is one more missing ingredient, attaining increasing recognition by research labs across the world, namely research software engineering. Traditionally seen as a professional service to support the implementation of computational models, research software engineering now emerges as an equal academic pillar to computational mathematics and data driven approaches. Software design, and hardware limitations, inform and shape the design of computational methods. Researchers need to take a holistic view across computational modelling and software engineering to create truly innovative solutions to the truly challenging problems from digital twins in personal medicine to simulating and mitigating the effects of climate change. This CDT has been designed around the need to train graduates across the interfaces of physics and data driven computational modelling and research software engineering. Our trainees will be able to engage with challenging problems not only from a modelling perspective but also from a software perspective, moving fluently across modelling and research software engineering. The subsequent urgent need for training in research software engineering at the highest level is also increasingly recognised by research centres across the world. We have partnered with a number of institutions in this proposal who follow this vision. In the UK this has been recently exemplified by the Independent Review of the Future of Compute, which recognised the importance of pairing infrastructure investments with skills programmes, and the importance of creating, attracting and retaining world class compute talent. Paired with an innovative training programme around interface working groups and software projects, our graduates will participate in and shape world leading research across the mathematics of data enhanced computational modelling, the design of corresponding computational algorithms, scientific research software engineering, and domain specific applications.

Probabilistic modelling permeates all branches of engineering and science, either in a fundamental way, addressing randomness and uncertainty in physical and economic phenomena, or as a device for the design of stochastic algorithms for data analysis, systems design and optimisation. Probability also provides the theoretical framework which underpins the analysis and design of algorithms in Data Science and Artificial Intelligence. The "CDT in Mathematics of Random Systems" is a new partnership in excellence between the Oxford Mathematical Institute, the Oxford Dept of Statistics, the Dept of Mathematics at Imperial College and multiple industry partners from the healthcare, technology and financial services sectors, whose goal is to establish an internationally leading PhD training centre for probability and its applications in physics, finance, biology and Data Science, providing a national beacon for research and training in stochastic modelling and its applications, reinforcing the UK's position as an international leader in this area and meeting the needs of industry for experts with strong analytical, computing and modelling skills. We bring together two of the worlds' best and foremost research groups in the area of probabilistic modelling, stochastic analysis and their applications -Imperial College and Oxford- to deliver a consolidated training programme in probability, stochastic analysis, stochastic simulation and computational methods and their applications in physics, biology, finance, healthcare and Data Science. Doctoral research of students will focus on the mathematical modelling of complex physical, economic and biological systems where randomness plays a key role, covering mathematical foundations as well as specific applications in collaboration with industry partners. Joint projects with industrial partners across several sectors -technology, finance, healthcare- will be used to sharpen research questions, leverage EPSRC funding and transfer research results to industry. Our vision is to educate the next generation of PhDs with unparalleled, cross-disciplinary expertise, strong analytical and computing skills as well as in-depth understanding of applications, to meet the increasing demand for such experts within the Technology sector, the Financial Service sector, the Healthcare sector, Government and other Service sectors, in partnership with industry partners from these sectors who have committed to co-funding this initiative. ALIGNMENT with EPSRC PRIORITIES This proposal reaches across various areas of pure and applied mathematics and Data Science and addresses the EPSRC Priority areas of (15. Mathematical and Computational Modelling), (22. Pure Mathematics and its Interfaces) ; however, the domain it covers is cross-disciplinary and broader than any of these priority areas taken in isolation. Probabilistic methods and algorithms form the theoretical foundation for the burgeoning area of Data Science and AI, another EPSRC Priority area which we plan to address, in particular through industry partnerships with AI/technology/data science firms. IMPACT By training highly skilled experts equipped to build, analyse and deploy probabilistic models, the CDT in Mathematics of Random Systems will contribute to - sharpening the UK's research lead in this area and training a new generation of mathematical scientists who can tackle scientific challenges in the modelling of complex, simulation and control of complex random systems in science and industry, and explore the exciting new avenues in mathematical research many of which have been pioneered by researchers in our two partner institutions; - train the next generation of experts able to deploy sophisticated data driven models and algorithms in the technology, finance and healthcare sectors