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Logics for Hybrid Systems
 Proceedings of the IEEE
, 2000
"... This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems ..."
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Cited by 138 (13 self)
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This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems
Differential Dynamic Logic for Hybrid Systems
, 2007
"... 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, ..."
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Cited by 76 (44 self)
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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 realvalued 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 wellsuited for verifying realistic hybrid systems with parametric system dynamics.
DifferentialAlgebraic Dynamic Logic for DifferentialAlgebraic Programs
"... Abstract. We generalise dynamic logic to a logic for differentialalgebraic programs, i.e., discrete programs augmented with firstorder differentialalgebraic formulas as continuous evolution constraints in addition to firstorder discrete jump formulas. These programs characterise interacting discr ..."
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Cited by 41 (27 self)
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Abstract. We generalise dynamic logic to a logic for differentialalgebraic programs, i.e., discrete programs augmented with firstorder differentialalgebraic formulas as continuous evolution constraints in addition to firstorder discrete jump formulas. These programs characterise interacting discrete and continuous dynamics of hybrid systems elegantly and uniformly. For our logic, we introduce a calculus over real arithmetic with discrete induction and a new differential induction with which differentialalgebraic programs can be verified by exploiting their differential constraints algebraically without having to solve them. We develop the theory of differential induction and differential refinement and analyse their deductive power. As a case study, we present parametric tangential roundabout maneuvers in air traffic control and prove collision avoidance in our calculus.
Process algebra for hybrid systems
 Theoretical Computer Science
, 2003
"... Abstract. We propose a process algebra obtained by extending a combination of the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, Chap. 4, 2002] and the process algebra with propositional signals from Baeten and ..."
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Cited by 38 (4 self)
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Abstract. We propose a process algebra obtained by extending a combination of the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, Chap. 4, 2002] and the process algebra with propositional signals from Baeten and
Formal Requirements Analysis of an Avionics Control System
 IEEE Transactions on Software Engineering
, 1997
"... We report on a formal requirements analysis experiment involving an avionics control system. We describe a method for specifying and verifying realtime systems with PVS. The experiment involves the formalization of the functional and safety requirements of the avionics system as well as its multile ..."
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Cited by 29 (1 self)
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We report on a formal requirements analysis experiment involving an avionics control system. We describe a method for specifying and verifying realtime systems with PVS. The experiment involves the formalization of the functional and safety requirements of the avionics system as well as its multilevel verification. First level verification demonstrates the consistency of the specifications whilst the second level shows that certain system safety properties are satisfied by the specification. We critically analyze methodological issues of large scale verification and propose some practical ways of structuring verification activities for optimising the benefits. KeywordsFormal specification, formal verification, safety critical systems, requirements analysis, avionics systems. I. Introduction T HIS paper reports on an experiment in the use of formal methods for producing and analyzing software requirements for a safetyrelated system. This work was conducted as part of the SafeFM ...
An Adequate First Order Interval Logic
 In COMPOS'97, volume 1536 of LNCS
, 1996
"... The paper uses left and right neighbourhoods as primitive interval modalities to define other unary and binary modalities of intervals in a first order logic with interval length. A complete first order logic for the neighbourhood modalities is presented. The paper demonstrates how the logic can sup ..."
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Cited by 25 (2 self)
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The paper uses left and right neighbourhoods as primitive interval modalities to define other unary and binary modalities of intervals in a first order logic with interval length. A complete first order logic for the neighbourhood modalities is presented. The paper demonstrates how the logic can support formal specification and verification of liveness and fairness, and also of various notions of real analysis. 1 Introduction Interval temporal logics, based on ITL [11], have shown to be useful for the specification and verification of safety properties of realtime systems. In these logics one can succinctly express properties like: "for all intervals of a given size, OE must hold", and "if OE holds for an interval, then there is a subinterval where / holds", and so on. However, these logics cannot express more abstract liveness properties like "eventually there is an interval where OE holds" and "OE will hold infinitely often in the future". The reason for this limitation is that the...
Modelling Status and Event Behaviour of Interactive Systems
, 1996
"... Interactive systems involve both events which occur at specific moments (e.g. keystrokes, mouseclicks and beeps) and more persistent status phenomena which can be observed at any time (e.g. the position of the mouse, the image on the screen). Most formalisms used for interactive systems concentrate ..."
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Cited by 22 (8 self)
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Interactive systems involve both events which occur at specific moments (e.g. keystrokes, mouseclicks and beeps) and more persistent status phenomena which can be observed at any time (e.g. the position of the mouse, the image on the screen). Most formalisms used for interactive systems concentrate on one aspect or another and may be asymmetric in their treatment of input and output. This paper classifies notations and models for interface specification by the way they treat status and event phenomena in their input and output. We use this to construct an model and associated notation which incorporates both. Specifying examples using this model highlights important design issues which would be missed if either status or event phenomena were not properly treated. 1
A Duration Calculus with Infinite Intervals
 In Fundamentals of Computation Theory, Horst Reichel (Ed.), pages 1641. LNCS 965
, 1995
"... Abstract. This paper introduces infinite intervals into the Duration Calculus [32]. The extended calculus defines a state duration over an infinite interval by a property which specifies the limit of the state duration over finite intervals, and excludes the description operator. Thus the calculus c ..."
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Cited by 16 (3 self)
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Abstract. This paper introduces infinite intervals into the Duration Calculus [32]. The extended calculus defines a state duration over an infinite interval by a property which specifies the limit of the state duration over finite intervals, and excludes the description operator. Thus the calculus can be established without involvement of unpleasant calculation of infinity. With limits of state durations, one can treat conventional liveness and fairness, and can also measure liveness and fairness through properties of limits. Including both finite and infinite intervals, the calculus can, in a simple manner, distinguish between terminating behaviour and nonterminating behaviour, and therefore directly specify and reason about sequentiality. 1
Logics of Dynamical Systems
"... We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded ..."
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Cited by 15 (15 self)
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We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded systems and cyberphysical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. Distributed hybrid systems combine distributed systems with hybrid systems, i.e., they are multiagent hybrid systems that interact through remote communication or physical interaction. Stochastic hybrid systems combine stochastic