Hybrid action systems

Rönkkö, Mauno; Ravn, Anders P.; Sere, Kaisa

doi:10.1016/s0304-3975(02)00547-9

Cited by 43 publications

(20 citation statements)

References 6 publications

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“…Rönkkö et al [53] extended guarded command programs with differential relations and gave a weakest-precondition semantics in higher-order logic with built-in derivatives. Without providing a means for verification of this higher-order logic, this approach is still limited to providing a notational variant of classical mathematics.…”

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confidence: 99%

Differential Dynamic Logic for Hybrid Systems

2008

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Hybrid systems are models for complex physical systems and are defined as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. With the goal of developing a theoretical and practical foundation for deductive verification of hybrid systems, we introduce a dynamic logic for hybrid programs, which is a program notation for hybrid systems. As a verification technique that is suitable for automation, we introduce a free variable proof calculus with a novel combination of real-valued free variables and Skolemisation for lifting quantifier elimination for real arithmetic to dynamic logic. The calculus is compositional, i.e., it reduces properties of hybrid programs to properties of their parts. Our main result proves that this calculus axiomatises the transition behaviour of hybrid systems completely relative to differential equations. In a case study with cooperating traffic agents of the European Train Control System, we further show that our calculus is well-suited for verifying realistic hybrid systems with parametric system dynamics.

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confidence: 99%

Differential Dynamic Logic for Hybrid Systems

2008

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“…Due to the simplicity of the model, action systems have been used as a basis for several theories of program refinement [3,4,7,41,46,50]. Part of the simplicity of action systems is due to the inherent interleaving semantics assumption, which ensures that statements are executed one after another (even under parallel composition), and hence, a concurrent system is viewed as a sequential program with a non-deterministic choice over all parallel actions.…”

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confidence: 99%

“…Unlike our model where time is implicitly advanced, Fidge and Wellings use a 'tick' action to model the passage of time, and accessibility restrictions are used to allow multiple processes to modify the same variable. Rönkkö et al extend action systems with actions that describe continuous changes to the state using differential equations [45,46]. A prioritised alternating model of execution is used to ensure that the (discrete) controller actions are able to execute.…”

Section: Related Workmentioning

confidence: 99%

Deriving real-time action systems with multiple time bands using algebraic reasoning

Dongol

Hayes

Derrick

2014

Science of Computer Programming

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The verify-while-develop paradigm allows one to incrementally develop programs from their specifications using a series of calculations against the remaining proof obligations. This paper presents a derivation method for real-time systems with realistic constraints on their behaviour. We develop a high-level intervalbased logic that provides flexibility in an implementation, yet allows algebraic reasoning over multiple granularities and sampling multiple sensors with delay. The semantics of an action system is given in terms of interval predicates and algebraic operators to unify the logics for an action system and its properties, which in turn simplifies the calculations and derivations.

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“…Rönkkö et al [26] presented a guarded command language with differential relations and gave a semantics in higher-order logic with built-in derivatives. Without providing a means for verification of this higher-order logic, the approach is still limited to providing a notational variant of classical mathematics.…”

Section: Introductionmentioning

confidence: 99%

Differential Dynamic Logic for Verifying Parametric Hybrid Systems

Platzer

Lecture Notes in Computer Science

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Abstract. We introduce a first-order dynamic logic for reasoning about systems with discrete and continuous state transitions, and we present a sequent calculus for this logic. As a uniform model, our logic supports hybrid programs with discrete and differential actions. For handling real arithmetic during proofs, we lift quantifier elimination to dynamic logic. To obtain a modular combination, we use side deductions for verifying interacting dynamics. With this, our logic supports deductive verification of hybrid systems with symbolic parameters and first-order definable flows. Using our calculus, we prove a parametric inductive safety constraint for speed supervision in a train control system.

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Hybrid action systems

Cited by 43 publications

References 6 publications

Differential Dynamic Logic for Hybrid Systems

Differential Dynamic Logic for Hybrid Systems

Deriving real-time action systems with multiple time bands using algebraic reasoning

Differential Dynamic Logic for Verifying Parametric Hybrid Systems

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