Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Cover of the book

2017 | OriginalPaper | Chapter

1. Transition Systems

Authors : Calin Belta, Boyan Yordanov, Ebru Aydin Gol

Published in: Formal Methods for Discrete-Time Dynamical Systems

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter, we define the syntax and semantics of transition systems, and provide several illustrative examples. In particular, we present different (deterministic, nondeterministic, finite, and infinite) transition system representations for discrete-time dynamical systems. We also introduce simulation and bisimulation relations, which are central for the construction of finite abstractions throughout the book.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
next chapter Temporal Logics and Automata
Footnotes
1
Since the \(Post\) operator was defined for a set of inputs, the correct notation here is \(Post_{T}(x,\{\sigma \})\). For simplicity, and with a slight abuse of notation, we omit the set notation when only a singleton input is considered. The same observation applies to the \(Pre\) operator.
 
2
As before, without the risk of confusion, and to keep the notation simple, we slightly abuse the notation when we refer to singletons and sets made of just one element. Formally, \(\delta \) outputs a set, while f outputs a singleton. In this case, the set produced by \(\delta \) has just one element.
 
Metadata
Title
Transition Systems
Authors
Calin Belta
Boyan Yordanov
Ebru Aydin Gol
Copyright Year
2017
Book
Formal Methods for Discrete-Time Dynamical Systems

Print ISBN: 978-3-319-50762-0

Electronic ISBN: 978-3-319-50763-7

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-50763-7_1