Refinement of time

We discuss mathematical models of the timed behaviour of system components. We study reactive system components that relate input-to-output streams. We work out a hierarchy of timing concepts. We distinguish non-timed streams, discrete streams with discrete or with continuous time, and dense streams with continuous time. We introduce a notion of a timed system component and formulate requirements for the time flow. We show how to compose timed systems in a modular way. We demonstrate that the introduction of time into a system model as well as the change of the timing model during the system development process can be captured as classical refinement steps.

[1]  Manfred Broy,et al.  Specification and Refinement of Finite Dataflow Networks - a Relational Approach , 1994, FTRTFT.

[2]  Nancy A. Lynch,et al.  Forward and Backward Simulations, II: Timing-Based Systems , 1991, Inf. Comput..

[3]  Niklaus Wirth,et al.  Toward a discipline of real-time programming , 1977, CACM.

[4]  C. A. R. Hoare,et al.  A Calculus of Durations , 1991, Inf. Process. Lett..

[5]  Nancy A. Lynch,et al.  A Proof of the Kahn Principle for Input/Output Automata , 1989, Inf. Comput..

[6]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[7]  Gérard Berry,et al.  Preemption in Concurrent Systems , 1993, FSTTCS.

[8]  Nancy A. Lynch,et al.  Forward and Backward Simulations, II: Timing-Based Systems , 1996, Inf. Comput..

[9]  Manfred Broy,et al.  Functional specification of time-sensitive communicating systems , 1993, TSEM.

[10]  David Harel,et al.  Statecharts: A Visual Formalism for Complex Systems , 1987, Sci. Comput. Program..

[11]  Hermann Kopetz,et al.  Sparse time versus dense time in distributed real-time systems , 1992, [1992] Proceedings of the 12th International Conference on Distributed Computing Systems.

[12]  Leslie Lamport,et al.  TIMESETS -- A New Method for Temporal Reasoning about Programs , 1981, Logic of Programs.

[13]  Nancy A. Lynch,et al.  Hierarchical correctness proofs for distributed algorithms , 1987, PODC '87.

[14]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[15]  Thomas F. Melham.  Higher Order Logic and Hardware Verification , 1993, Cambridge Tracts in Theoretical Computer Science.

[16]  Prakash Panangaden,et al.  The Expressive Power of Indeterminate Dataflow Primitives , 1992, Inf. Comput..

[17]  Gérard Berry,et al.  The Esterel Synchronous Programming Language: Design, Semantics, Implementation , 1992, Sci. Comput. Program..

[18]  Arthur J. Bernstein,et al.  Proving real-time properties of programs with temporal logic , 1981, SOSP.

[19]  David Michael Ritchie Park,et al.  On the Semantics of Fair Parallelism , 1979, Abstract Software Specifications.

[20]  Manfred Broy,et al.  Denotational Semantics of Communicating Processes Based on a Language for Applicative Multiprogramming , 1983, Inf. Process. Lett..

[21]  Olaf Müller,et al.  Functional Specification of Real-Time and Hybrid Systems , 1997, HART.

[22]  Manfred Broy,et al.  Applicative Real-Time Programming , 1983, IFIP Congress.

[23]  Itu-T.  Specification and Description Language (SDL) , 1999 .