The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.

This book provides an overview of the confluence of ideas in Turing’s era and work and examines the impact of his work on mathematical logic and theoretical computer science. It combines contributions by well-known scientists on the history and philosophy of computability theory as well as on generalised Turing computability. By looking at the roots and at the philosophical and technical influence of Turing’s work, it is possible to gather new perspectives and new research topics which might be considered as a continuation of Turing’s working ideas well into the 21st century.

The book presents a remarkable collection of chapters covering a wide range of topics in the areas of intelligent systems and artificial intelligence, and their real-world applications. It gathers the proceedings of the Intelligent Systems Conference 2019, which attracted a total of 546 submissions from pioneering researchers, scientists, industrial engineers, and students from all around the world. These submissions underwent a double-blind peer-review process, after which 190 were selected for inclusion in these proceedings. As intelligent systems continue to replace and sometimes outperform human intelligence in decision-making processes, they have made it possible to tackle a host of problems more effectively. This branching out of computational intelligence in several directions and use of intelligent systems in everyday applications have created the need for an international conference as a venue for reporting on the latest innovations and trends. This book collects both theory and application based chapters on virtually all aspects of artificial intelligence; presenting state-of-the-art intelligent methods and techniques for solving real-world problems, along with a vision for future research, it represents a unique and valuable asset.

Professor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for “his advancement of our understanding of the complexity of computation in a significant and profound way.” This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook’s synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook’s ideas and their enduring impact on the research community. The book also contains biographical material, Cook’s Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.

Traditionally, models and methods for the analysis of the functional correctness of reactive systems, and those for the analysis of their performance (and - pendability) aspects, have been studied by di?erent research communities. This has resulted in the development of successful, but distinct and largely unrelated modeling and analysis techniques for both domains. In many modern systems, however, the di?erence between their functional features and their performance properties has become blurred, as relevant functionalities become inextricably linked to performance aspects, e.g. isochronous data transfer for live video tra- mission. During the last decade, this trend has motivated an increased interest in c- bining insights and results from the ?eld of formal methods – traditionally - cused on functionality – with techniques for performance modeling and analysis. Prominent examples of this cross-fertilization are extensions of process algebra and Petri nets that allow for the automatic generation of performance models, the use of formal proof techniques to assess the correctness of randomized - gorithms, and extensions of model checking techniques to analyze performance requirements automatically. We believe that these developments markthe - ginning of a new paradigm for the modeling and analysis of systems in which qualitative and quantitative aspects are studied from an integrated perspective. We are convinced that the further worktowards the realization of this goal will be a growing source of inspiration and progress for both communities.

This Festschrift volume, dedicated to Jifeng He on the occasion of his 80th birthday, includes refereed papers by leading researchers, many of them current and former colleagues, presented at a dedicated celebration in the Shanghai Science Hall in September 2023. Jifeng was an important researcher on the European ESPRIT ProCoS project and the Working Group on Provably Correct Systems, subsequently he collaborated with Tony Hoare on Unifying Theories of Programming. Jifeng returned to China in 1998, first to the United Nations University in Macau and then to the East China Normal University in Shanghai. He has since founded an Artificial Intelligence research institute that focuses on the application of technology in large-scale industrial software systems. His scientific contributions have been recognized through his election to membership of the Chinese Academy of Sciences. The first paper in the volume provides an overview of Jifeng’s research contributions, especially in the area of formal methods, and the following two papers detail developments in UTP and rCOS (refinement calculus of object systems). In the next two sections of the book, the editors included papers by colleagues and coauthors of Jifeng while he was at the University of Oxford and engaged with the European ProCoS project. The section that follows includes papers authored by colleagues from his later research in China and Europe. The final section includes a paper related to Jifeng’s recent roadmap for UTP.

This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary.