Algorithmic Algebraic Model Checking II: Decidability of Semi-algebraic Model Checking and Its Applications to Systems Biology

Mysore, Venkatesh; Piazza, Carla; Mishra, Bhubaneswar

doi:10.1007/11562948_18

Cited by 31 publications

(23 citation statements)

References 24 publications

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“…They have been used successfully in model checking [1,6,14,15,18] of finite-state system abstractions. Continuous state spaces of hybrid systems, however, often do not admit equivalent finite-state abstractions [14,18]. Instead of model checking, TL can also be used deductively to prove validity of formulas in calculi [8,9].…”

Section: Introductionmentioning

confidence: 99%

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A Temporal Dynamic Logic for Verifying Hybrid System Invariants

Platzer

Logical Foundations of Computer Science

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Abstract. We combine first-order dynamic logic for reasoning about possible behaviour of hybrid systems with temporal logic for reasoning about the temporal behaviour during their operation. Our logic supports verification of hybrid programs with first-order definable flows and provides a uniform treatment of discrete and continuous evolution. For our combined logic, we generalise the semantics of dynamic modalities to refer to hybrid traces instead of final states. Further, we prove that this gives a conservative extension of dynamic logic. On this basis, we provide a modular verification calculus that reduces correctness of temporal behaviour of hybrid systems to non-temporal reasoning. Using this calculus, we analyse safety invariants in a train control system and symbolically synthesise parametric safety constraints.

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Section: Introductionmentioning

confidence: 99%

“…Mysore et al [18] analysed model checking of TCTL [1] properties for semialgebraic hybrid systems and proved undecidability. Our logic internalises operational models and supports multiple parametric systems.…”

Section: Introductionmentioning

confidence: 99%

A Temporal Dynamic Logic for Verifying Hybrid System Invariants

Platzer

Logical Foundations of Computer Science

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“…Likewise, it is difficult to read off the parameter constraints that are required for correctness from a failed verification attempt of model checkers [6][7][8], since concrete numeric values of a counterexample trace cannot simply be translated into a generic constraint on the free parameters of the system which would have prevented this kind of error. While approaches like counterexample-guided abstraction refinement [9,8] are highly efficient in undoing automatic abstractions of an abstract hybrid system from spurious counterexamples, they stop when true counterexamples remain in the concrete system.…”

Section: Introductionmentioning

confidence: 99%

“…Other approaches [13,7] use quantifier elimination for model checking hybrid automata. We use the same decision procedure for handling arithmetics and generalize these results adding free parameter constraint handling and discovery.…”

Section: Introductionmentioning

confidence: 99%

“…We use the same decision procedure for handling arithmetics and generalize these results adding free parameter constraint handling and discovery. In [7] real quantifier elimination is used for model checking TCTL properties of semi-algebraic hybrid systems. However, they use approximated solutions of the differential equations, whereas our approach avoids those approximation errors.…”

Section: Introductionmentioning

confidence: 99%

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European Train Control System: A Case Study in Formal Verification

Platzer

Quesel

2009

Lecture Notes in Computer Science

105

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Abstract. Complex physical systems have several degrees of freedom. They only work correctly when their control parameters obey corresponding constraints. Based on the informal specification of the European Train Control System (ETCS), we design a controller for its cooperation protocol. For its free parameters, we successively identify constraints that are required to ensure collision freedom. We formally prove the parameter constraints to be sharp by characterizing them equivalently in terms of reachability properties of the hybrid system dynamics. Using our deductive verification tool KeYmaera, we formally verify controllability, safety, liveness, and reactivity properties of the ETCS protocol that entail collision freedom. We prove that the ETCS protocol remains correct even in the presence of perturbation by disturbances in the dynamics. We verify that safety is preserved when a PI controlled speed supervision is used.

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