Operational Semantics for Timed Systems

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

  • Heinrich Rust

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

Table of contents

  1. Front Matter
    Pages I-XII
  2. Overview

    1. Heinrich Rust
      Pages 1-3
  3. Basic Concepts

    1. Front Matter
      Pages 13-13
    2. Heinrich Rust
      Pages 15-22
    3. Heinrich Rust
      Pages 23-29
    4. Heinrich Rust
      Pages 31-48
    5. Heinrich Rust
      Pages 49-62
    6. Heinrich Rust
      Pages 63-72
  4. Modelling Strategies

    1. Front Matter
      Pages 73-73
    2. Heinrich Rust
      Pages 75-82
    3. Heinrich Rust
      Pages 83-95
    4. Heinrich Rust
      Pages 97-106
    5. Heinrich Rust
      Pages 107-112
    6. Heinrich Rust
      Pages 113-127
  5. Applications

    1. Front Matter
      Pages 129-129
    2. Heinrich Rust
      Pages 131-139
    3. Heinrich Rust
      Pages 141-159
    4. Heinrich Rust
      Pages 173-201
  6. Summary

    1. Front Matter
      Pages 203-203
    2. Heinrich Rust
      Pages 205-209
  7. Back Matter
    Pages 211-223

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).


abstract state machines algorithms continuous time systems discrete time systems hybrid systems modeling non-standard analysis non-standard timed abstract state machines operational semantics temporal logics timed Petri nets timed automata timed systems

Authors and affiliations

  • Heinrich Rust
    • 1
  1. 1.Software-SystemtechnikBTU CottbusCottbusGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science Computer Science (R0)
  • Print ISBN 978-3-540-25576-5
  • Online ISBN 978-3-540-32008-1
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349
  • Buy this book on publisher's site
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