Duration Calculus

Real-time systems are systems in which temporal properties areessential for reliability and correctness. Examples of systems wherecorrectness and reliability are important for safety reasons includecontrol systems for cars, trains and air planes. In devices such aswashing machines, DVD players and mobile phones the correctness andreliability of the embedded real-time computing systems are importantfor economical reasons as it is expensive to repair errors after theproduction phase.§Duration Calculus is an interval logic having special features forexpressing and analysing time durations of states in real-timesystems. Duration Calculus represents a formal approach to thedevelopment of real-time systems, where requirements and designs canbe expressed and reasoned about at an appropriate level ofabstraction.§This book presents the logical foundations of Duration Calculus in acoherent and thorough manner and through selective case studies itexpains how Durations Calculus can be applied to formal specificationand verification of real-time systems. The book also contains anextensive survey of the research on Duration Calculus.§Material included in the book has been used for M.Sc. andPh.D. courses, but the book is also valuable for experiencedresearchers and professionals.A comprehensive introduction to interval logic and duration calculus for modelling, analysing and verifying real-time systems. The Duration Calculus (DC) represents a logical approach to formal design of real-time systems. In DC real numbers are used to model time and Boolean-valued (i.e. {0,1}-valued) functions over time to model states of real-time systems. The duration of a state in a time interval is the accumulated presence time of the state in the interval. DC extends interval logic to a calculus to specify and reason about properties of state durations. The text covers theory (completeness, decidability, undecidability, model-checking), results, as well as case studies (Deadline Driven Scheduler).Duration calculus constitutes a formal approach to the development of real-time systems; as an interval logic with special features for expressing and analyzing time durations of states in real-time systems, it allows for representing and formally reasoning about requirements and designs at an appropriate level of abstraction.§This book presents the logical foundations of duration calculus in a coherent and thorough manner. Through selective case studies it explains how duration calculus can be applied to the formal specification and verification of real-time systems. The book also contains an extensive survey of the current research in this field.§The material included in this book has been used for graduate and postgraduate courses, while it is also suitable for experienced researchers and professionals.