Book ChapterDOI
Exact symbolic models for verification
Paulo Tabuada
- pp 73-111
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TLDR
Most of the abstraction techniques described in this chapter require linear differential equations and it is discussed as a special topic how to transform a class of nonlinear differential equations into linear di_erential equations in larger state spaces.Abstract:
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.read more
Citations
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Book ChapterDOI
Temporal Logic Verification of Stochastic Systems Using Barrier Certificates
TL;DR: This paper presents a methodology for temporal logic verification of discrete-time stochastic systems by decomposing the negation of the specification into a union of sequential reachabilities and then using barrier certificates to compute upper bounds for these reachability probabilities.
Journal ArticleDOI
Route Guidance for Satisfying Temporal Logic Specifications on Aircraft Motion
TL;DR: The main result of this paper is the precise characterization of acceptable routes that are guaranteed to be traversable by admissible state trajectories of the aircraft model while satisfying the given linear temporal logic specifications.