Communicating sequential processes
Communicating sequential processes
Safety analysis of timing properties in real-time systems
IEEE Transactions on Software Engineering - Special issue on reliability and safety in real-time process control
Programming from specifications
Programming from specifications
A framework for building dependable systems
The Computer Journal - Special issue on methodologies (systems and software)
The Z notation: a reference manual
The Z notation: a reference manual
The RAISE specification language
The RAISE specification language
Embedding time granularity in a logical specification language for synchronous real-time systems
6IWSSD Selected Papers of the Sixth International Workshop on Software Specification and Design
Journal of the ACM (JACM)
Real-time logics: complexity and expressiveness
Information and Computation - Special issue: selections from 1990 IEEE symposium on logic in computer science
Theoretical Computer Science
A classical mind
A classical mind
The benefits of relaxing punctuality
Journal of the ACM (JACM)
Using Z: specification, refinement, and proof
Using Z: specification, refinement, and proof
UPPAAL—a tool suite for automatic verification of real-time systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Timewise refinement for communicating processes
Science of Computer Programming
IEEE Transactions on Software Engineering - Special issue on formal methods in software practice
An axiomatic basis for computer programming
Communications of the ACM
The Theory and Practice of Concurrency
The Theory and Practice of Concurrency
Concurrent and Real Time Systems: The CSP Approach
Concurrent and Real Time Systems: The CSP Approach
Towards a Time Model for Circus
ICFEM '02 Proceedings of the 4th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
Action Transducers and Timed Automata
CONCUR '92 Proceedings of the Third International Conference on Concurrency Theory
An Operational Semantics for Timed RAISE
FM '99 Proceedings of the Wold Congress on Formal Methods in the Development of Computing Systems-Volume II
Temporalized logics and automata for time granularity
Theory and Practice of Logic Programming
Representing and Reasoning about Temporal Granularities
Journal of Logic and Computation
Spin model checker, the: primer and reference manual
Spin model checker, the: primer and reference manual
IEEE Transactions on Software Engineering
Formal Aspects of Computing
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
A process algebraic framework for specification and validation of real-time systems
Formal Aspects of Computing
A timeband framework for modelling real-time systems
Real-Time Systems
The miracle of reactive programming
UTP'08 Proceedings of the 2nd international conference on Unifying theories of programming
A Timed Model of Circus with the Reactive Design Miracle
SEFM '10 Proceedings of the 2010 8th IEEE International Conference on Software Engineering and Formal Methods
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Complex real-time systems exhibit dynamic behaviours on many different time levels. To cope with the wide range of time scales and produce more dependable computer-based systems, we develop a Timebands model that can explicitly recognise a finite set of distinct time bands in which temporal properties and associated behaviours are described. In order to formalise the Timebands model, we propose a new timed model, named Timed Circus, of Circus, which is the combination of Z, CSP, and the refinement calculus in the setting of Unifying Theories of Programming. Different from most approaches such as Timed CSP, Timed Circus uses a complete lattice in the implication ordering to model the distinctive features of the Timebands model. As a result, the semantics of the Timebands model is built upon Timed Circus to guarantee soundness of each operator and maintain consistency and coordination between different time bands. By means of two small systems, we demonstrate how the Timebands model contributes to describing complex real-time systems with multiple time scales.