A Temporal Dynamic Logic for Verifying Hybrid System Invariants

Platzer, André

doi:10.1007/978-3-540-72734-7_32

Cited by 25 publications

(56 citation statements)

References 23 publications

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“…Otherwise, dL can be augmented with temporal operators to refer to intermediate states or nonterminating traces. The corresponding calculus is compatible and reduces temporal properties to non-temporal properties at intermediate states of the hybrid program [49].…”

Section: Definition 5 (Transition Semantics Of Hybrid Programs)mentioning

confidence: 99%

“…Further, this constraint can be used to find out how dense a track can be packed with trains in order to maximise ETCS throughput without endangering safety. Using the dL calculus, similar constraints can be derived [49] to find out how early a train needs to start negotiation in order to minimise the risk of having to reduce speed when the MA is not extendable in time, which is the ST parameter of Fig. 4.…”

Section: Verifying Safety In the European Train Control Systemmentioning

confidence: 99%

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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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Section: Definition 5 (Transition Semantics Of Hybrid Programs)mentioning

confidence: 99%

Section: Verifying Safety In the European Train Control Systemmentioning

confidence: 99%

Differential Dynamic Logic for Hybrid Systems

2008

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“…Like model checking, first-order DL can analyse the behaviour of operational system models [22,23]. Yet, DL calculi accept parameters: they verify systems by deductive proof rather than a more enumerative and graph-theoretic analysis of the (abstract) state space as in model checking [7].…”

Section: Introductionmentioning

confidence: 99%

“…In [23,24], we have introduced logics that extend the basic ideas of [22] into different directions. In [24], we have presented a logic with nominals to investigate compositionality.…”

Section: Introductionmentioning

confidence: 99%

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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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Embedding CCSL into Dynamic Logic: A Logical Approach for the Verification of CCSL Specifications

Zhang¹,

Wu²,

Chen³

et al. 2019

Communications in Computer and Information Science

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The Clock Constraint Specification Language (CCSL) is a clock-based specification language for capturing causal and chronometric constraints between events in Real-Time Embedded Systems (RTESs). Due to the limitations of the existing verification approaches, CCSL lacks a full verification support for 'unsafe CCSL specifications' and a unified proof framework. In this paper, we propose a novel verification approach based on theorem proving and SMT-checking. We firstly build a logic called CCSL Dynamic Logic (CDL), which extends the traditional dynamic logic with 'signals' and 'clock relations' as primitives, and with synchronous execution mechanism for modelling RTESs. Then we propose a sound and relatively complete proof system for CDL to provide the verification support. We show how CDL can be used to capture RTES and verify CCSL specifications by analyzing a simple case study.

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A Temporal Dynamic Logic for Verifying Hybrid System Invariants

Cited by 25 publications

References 23 publications

Differential Dynamic Logic for Hybrid Systems

Differential Dynamic Logic for Hybrid Systems

Differential Dynamic Logic for Verifying Parametric Hybrid Systems

Embedding CCSL into Dynamic Logic: A Logical Approach for the Verification of CCSL Specifications

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