Duration Calculus

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).

Comprehensive introduction to interval logic and duration calculus, for modelling, analysing and verifying real-time systems Covers theory (completeness, decidability, undecidability, model-checking) results, as well as case studies (Deadline Driven Scheduler) Contains chapters which point to further research (Probabilistic DC, Neighbourhood logic) Includes supplementary material: sn.pub/extras

Autorentext

Professor ZHOU Chaochen, Institute of Software, Chinese Academy of Sciences. Members of Chinese Academy of Sciences and the Third World Academy of Sciences. Former Director of International Institute for Software Technology, United Nations University. He has had about 30 years research experience in the area of formal techniques for computing systems, in particular for distributed and real-time systems.

Associate Prof. Michael R. Hansen. Informatics and Mathematical Modelling, Technical University of Denmark
Research interests:
Formal Methods, Computer Based Systems, Real-time systems, Hybrid systems, Duration Calculus.

Klappentext

Real-time systems are systems in which temporal properties are
essential for reliability and correctness. Examples of systems where
correctness and reliability are important for safety reasons include
control systems for cars, trains and air planes. In devices such as
washing machines, DVD players and mobile phones the correctness and
reliability of the embedded real-time computing systems are important
for economical reasons as it is expensive to repair errors after the
production phase.

Duration Calculus is an interval logic having special features for
expressing and analysing time durations of states in real-time
systems. Duration Calculus represents a formal approach to the
development of real-time systems, where requirements and designs can
be expressed and reasoned about at an appropriate level of
abstraction.

This book presents the logical foundations of Duration Calculus in a
coherent and thorough manner and through selective case studies it
expains how Durations Calculus can be applied to formal specification
and verification of real-time systems. The book also contains an
extensive survey of the research on Duration Calculus.

Material included in the book has been used for M.Sc. and
Ph.D. courses, but the book is also valuable for experienced
researchers and professionals.

Inhalt

1. Introduction.- 2. Interval Logic.- 3. Duration Calculus.- 4. Deadline-Driven Scheduler.- 5. Relative Completeness.- 6. Decidability.- 7. Undecidability.- 8. Model Checking: Linear Duration Invariants.- 9. State Transitions and Events.- 10. Superdense State Transitions.- 11. Neighborhood Logic.- 12. Probabilistic Duration Calculus.- References.- Abbreviations.- Symbol Index.