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Operational Semantics for Timed Systems

A Non-standard Approach to Uniform Modeling of Timed and Hybrid Systems

  • Book
  • © 2005

Overview

Authors:
  1. Heinrich Rust

    1. Software-Systemtechnik, BTU Cottbus, Cottbus, Germany

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Part of the book series: Lecture Notes in Computer Science (LNCS, volume 3456)

Part of the book sub series: Programming and Software Engineering (LNPSE)

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Table of contents (17 chapters)

  1. Front Matter

    Pages I-XII
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  2. Overview

    1. Overview

      • Heinrich Rust
      Pages 1-3

    2. Context: Formal Methods in Software Engineering

      • Heinrich Rust
      Pages 5-12

  3. Basic Concepts

    1. Front Matter

      Pages 13-13
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    2. Models of Time and of System Behaviors

      • Heinrich Rust
      Pages 15-22

    3. Infinitesimals

      • Heinrich Rust
      Pages 23-29

    4. Operational Semantics of Discrete Systems

      • Heinrich Rust
      Pages 31-48

    5. Defining Hybrid Systems with ASMs

      • Heinrich Rust
      Pages 49-62

    6. A Notation for a Temporal Logic

      • Heinrich Rust
      Pages 63-72

  4. Modelling Strategies

    1. Front Matter

      Pages 73-73
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    2. Concurrency and Reactivity: Interleaving

      • Heinrich Rust
      Pages 75-82

    3. The Synchronous Approach to Concurrency

      • Heinrich Rust
      Pages 83-95

    4. Deadlines

      • Heinrich Rust
      Pages 97-106

    5. Open Systems

      • Heinrich Rust
      Pages 107-112

    6. Making Use of Different Magnitudes of Reals

      • Heinrich Rust
      Pages 113-127

  5. Applications

    1. Front Matter

      Pages 129-129
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    2. A Case Study: Fischer’s Protocol

      • Heinrich Rust
      Pages 131-139

    3. An ASM Meta-model for Petri Nets with Timing

      • Heinrich Rust
      Pages 141-159

    4. An ASM Meta-model for Timed and Hybrid Automata

      • Heinrich Rust
      Pages 161-172

    5. A Production Cell with Timing

      • Heinrich Rust
      Pages 173-201
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Keywords

About this book

This monograph is dedicated to a novel approach for uniform modelling of timed and hybrid systems. Heinrich Rust presents a time model which allows for both the description of discrete time steps and continuous processes with a dense real-number time model. The proposed time model is well suited to express synchronicity of events in a real-number time model as well as strict causality by using uniform discrete time steps. Thus it integrates and reconciles two views of time that are commonly used separately in di?erent application domains. In many discrete systems time is modelled by discrete steps of uniform length, in continuous systems time is seen as a dense ?ow. Themainideatointegratethesedi?erentviewsisadiscretizationofthedense real-number time structure by using constant in?nitesimal time steps within each real-number point in time. The underlying mathematical structure of this time model is based on concepts of Non-standard Analysis as proposed by Abraham Robinson in the 1950s. The discrete modelling, i.e., the descr- tion of sequential discrete algorithms at di?erent abstraction levels, is done with Abstract State Machines along the formalisms developed by Yuri Gu- vich and temporal logic. These ingredients produce a rich formal basis for describing a large variety of systems with quantitative linear time prop- ties, by seamless integration, re?nement and embedding of continuous and discrete models into one uniform semantic framework called“Non-standard Timed Abstract State Machines”(NTASM).

Authors and Affiliations

  • Software-Systemtechnik, BTU Cottbus, Cottbus, Germany

    Heinrich Rust

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