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From Control Law Diagrams to Ada via Circus
 In FM 2006
, 2006
"... Control engineers make extensive use of diagrammatic notations; control law diagrams are used in industry every day. Techniques and tools for analysis of these diagrams or their models are plentiful; verification of code created to implement them, however, is a challenge that has been taken up by fe ..."
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Control engineers make extensive use of diagrammatic notations; control law diagrams are used in industry every day. Techniques and tools for analysis of these diagrams or their models are plentiful; verification of code created to implement them, however, is a challenge that has been taken up by few. Our work is based on industrial tools that produce partial Z and CSP models of discretetime Simulink diagrams, and on Circus, a notation that combines Z, CSP, and a refinement calculus. We present a strategy to translate Simulink diagrams to Circus, and a strategy to prove that a parallel Ada implementation refines the specification of a diagram; we rely on a Circus semantics for the program. By using a combined notation, we provide a specification that considers both functional and behavioural aspects of a larger set of diagrams, and support verification of a larger number of implementations. We can handle, for instance, arbitrarily large data types and dynamic scheduling. 1
Coinductive Proofs for Streams in PVS ⋆
"... Abstract. WepresentanimplementationinthetheoremproverPVS of coinductive stream calculus. Stream calculus can be used to model signal flow graphs, and thus provides a nice mathematical foundation for reasoning about properties of signal flow graphs, which are again used to model a variety of systems ..."
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Abstract. WepresentanimplementationinthetheoremproverPVS of coinductive stream calculus. Stream calculus can be used to model signal flow graphs, and thus provides a nice mathematical foundation for reasoning about properties of signal flow graphs, which are again used to model a variety of systems such as digital signal processing. We show how proofs by coinduction are used to prove equality of streams, and present a strategy to do this automatically. 1
Automated verification of continuous and hybrid dynamical systems
, 2014
"... The standard method used for verifying the behaviour of a dynamical system is simulation. But simulation can check only a finite number of operating conditions and system parameters, leading to a potentially incomplete verification result. This dissertation presents several automated theorem proving ..."
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The standard method used for verifying the behaviour of a dynamical system is simulation. But simulation can check only a finite number of operating conditions and system parameters, leading to a potentially incomplete verification result. This dissertation presents several automated theorem proving based methods that can, in contrast to simulation, completely guarantee the safety of a dynamical system model. To completely verify a purely continuous dynamical system requires proving a universally quantified first order conjecture, which represents all possible trajectories of the system. Such a closed form solution may contain transcendental functions, rendering the problem undecidable in the general case. The automated theorem prover MetiTarski can be used to solve such a problem by reducing it to one over the real closed fields. The main issue is the doubly exponential complexity of the backend decision procedures that it depends on. This dissertation proposes several techniques that make the required conjectures eas