Exact symbolic models for verification

  • Paulo Tabuada


The evolution of physical quantities such as position, temperature, humidity, etc, is usually described by differential equations with solutions evolving on \({\mathbb R}^n\) or appropriate subsets. The infinite cardinality of \({\mathbb R}^n\) prevents a direct application of the verification methods described in Chapter 5. However, verification algorithms are still applicable whenever suitable finite-state abstractions of these infinite-state systems can be constructed. In recent years, several methods have been proposed for the construction of these abstractions based on a very interesting blend of different mathematical techniques. We present several of these methods starting with timed automata to illustrate the general principles of the abstraction process. Most of the abstraction techniques described in this chapter require linear differential equations. For this reason, we discuss as a special topic how to transform a class of nonlinear differential equations into linear di_erential equations in larger state spaces.


Equivalence Class Equivalence Relation Erential Equation Discrete Transition Unsafe State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of California, Los AngelesLos AngelesUSA

Personalised recommendations