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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Belta, C., Yordanov, B., Aydin Gol, E. (2017). Transition Systems. In: Formal Methods for Discrete-Time Dynamical Systems. Studies in Systems, Decision and Control, vol 89. Springer, Cham. https://doi.org/10.1007/978-3-319-50763-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-50763-7_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50762-0
Online ISBN: 978-3-319-50763-7
eBook Packages: EngineeringEngineering (R0)