Models that include a notion of time are ubiquitous in disciplines such as the natural sciences, engineering, philosophy, and linguistics, but in computing the abstractions provided by the traditional models are problematic and the discipline has spawned many novel models.

Chap. 1 It's About Time.- Chap. 2 Languages and Interpretations.- Chap. 3 Dimensions of the Time Modeling Problem.- Chap. 4 Dynamical Systems.- Chap. 5 Time in Hardware Modeling and Design.- Chap. 6 Time in the Analysis of Algorithms.- Chap. 7 Synchronous Abstract Machines.- Chap. 8 Asynchronous Abstract Machines: Petri Nets.- Chap. 9 Logic-Based Formalisms.- Chap. 10 Algebraic Formalisms.- Chap. 11 Dual-Language Approaches.- Chap. 12 Time Is up.- References.- Index.

Models that include a notion of time are ubiquitous in disciplines such as the natural sciences, engineering, philosophy, and linguistics, but in computing the abstractions provided by the traditional models are problematic and the discipline has spawned many novel models. This book is a systematic thorough presentation of the results of several decades of research on developing, analyzing, and applying time models to computing and engineering. After an opening motivation introducing the topics, structure and goals, the authors introduce the notions of formalism and model in general terms along with some of their fundamental classification criteria. In doing so they present the fundamentals of propositional and predicate logic, and essential issues that arise when modeling time across all types of system. Part I is a summary of the models that are traditional in engineering and the natural sciences, including fundamental computer science: dynamical systems and control theory; hardware design; and software algorithmic and complexity analysis. Part II covers advanced and specialized formalisms dealing with time modeling in heterogeneous software-intensive systems: formalisms that share finite state machines as common “ancestors”; Petri nets in many variants; notations based on mathematical logic, such as temporal logic; process algebras; and “dual-language approaches” combining two notations with different characteristics to model and verify complex systems, e.g., model-checking frameworks. Finally, the book concludes with summarizing remarks and hints towards future developments and open challenges. The presentation uses a rigorous, yet not overly technical, style, appropriate for readers with heterogeneous backgrounds, and each chapter is supplemented with detailed bibliographic remarks and carefully chosen exercises of varying difficulty and scope. The book is aimed at graduate students and researchers in computer science, whileresearchers and practitioners in other scientific and engineering disciplines interested in time modeling with a computational flavor will also find the book of value, and the comparative and conceptual approach makes this a valuable introduction for non-experts. The authors assume a basic knowledge of calculus, probability theory, algorithms, and programming, while a more advanced knowledge of automata, formal languages, and mathematical logic is useful.

Comparative and conceptual approach make this a valuable introduction for non-experts Organized presentation of issues that recur in computer science and other branches of engineering and science Exercises considered optional on first reading but then are necessary to understand the most subtle aspects of the presentation Includes supplementary material: sn.pub/extras Includes supplementary material: sn.pub/extras

GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com