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Relational Abstractions For Continuous and Hybrid Systems
"... Abstract. There has been much recent progress on invariant generation techniques for continuous systems whose dynamics are described by Ordinary Differential Equations (ODE). In this paper, we present a simple abstraction scheme for hybrid systems that abstracts continuous dynamics by relating any s ..."
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Abstract. There has been much recent progress on invariant generation techniques for continuous systems whose dynamics are described by Ordinary Differential Equations (ODE). In this paper, we present a simple abstraction scheme for hybrid systems that abstracts continuous dynamics by relating any state of the system to a state that can potentially be reached at some future time instant. Such relations are then interpreted as discrete transitions that model the continuous evolution of states over time. We adapt templatebased invariant generation techniques for continuous dynamics to derive relational abstractions for continuous systems with linear as well as nonlinear dynamics. Once a relational abstraction hasbeen derived,theresultingsystemis apurelydiscrete, infinitestatesystem. Therefore, techniquessuchas kinductioncan be directly applied to this abstraction to prove properties, and bounded modelchecking techniques applied to find potential falsifications. We present the basic underpinnings of our approach and demonstrate its use on many benchmark systems to derive simple and usable abstractions. 1
Beautiful interpolants
 In CAV
, 2013
"... Abstract. We describe a compositional approach to Craig interpolation based on the heuristic that simpler proofs of special cases are more likely to generalize. The method produces simple interpolants because it is able to summarize a large set of cases using one relatively simple fact. In particul ..."
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Abstract. We describe a compositional approach to Craig interpolation based on the heuristic that simpler proofs of special cases are more likely to generalize. The method produces simple interpolants because it is able to summarize a large set of cases using one relatively simple fact. In particular, we present a method for finding such simple facts in the theory of linear rational arithmetic. This makes it possible to use interpolation to discover inductive invariants for numerical programs that are challenging for existing techniques. We show that in some cases, the compositional approach can also be more efficient than traditional lazy SMT as a decision procedure. 1
HybridSAL Relational Abstracter
"... Abstract. In this paper, we present the HybridSAL relational abstracter – a tool for verifying continuous and hybrid dynamical systems. The input to the tool is a model of a hybrid dynamical system and a safety property. The output of the tool is a discrete state transition system and a safety prope ..."
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Abstract. In this paper, we present the HybridSAL relational abstracter – a tool for verifying continuous and hybrid dynamical systems. The input to the tool is a model of a hybrid dynamical system and a safety property. The output of the tool is a discrete state transition system and a safety property. The correctness guarantee provided by the tool is that if the output property holds for the output discrete system, then the input property holds for the input hybrid system. The input is in HybridSal input language and the output is in SAL syntax. The SAL model can be verified using the SAL tool suite. This paper describes the HybridSAL relational abstracter – the algorithms it implements, its input, its strength and weaknesses, and its use for verification using the SAL infinite bounded model checker and kinduction prover. 1
Refining Abstractions of Hybrid Systems Using Counterexample Fragments
 In Hybrid Systems: Computation and Control (HSCC’05), volume 3414 of Lect. Notes Comput. Sci
"... Counterexample guided abstraction refinement, a powerful technique for verifying properties of discretestate systems [4, 9] has been extended recently to hybrid systems verification [1, 3]. Unlike in discrete systems, however, establishing the successor relation for hybrid systems can be a fairl ..."
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Cited by 9 (3 self)
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Counterexample guided abstraction refinement, a powerful technique for verifying properties of discretestate systems [4, 9] has been extended recently to hybrid systems verification [1, 3]. Unlike in discrete systems, however, establishing the successor relation for hybrid systems can be a fairly expensive step since it requires evaluation and overapproximation of the continuous dynamics.
Generation of all counterexamples for pushdown systems
 In Proceedings of FORTE
, 2003
"... Abstract. We present a new, onthefly algorithm that, given a pushdown system model representing a sequential program with (recursive) procedure calls and an extended finitestate automaton representing (the negation of) a safety property, produces a succinct, symbolic representation of all counte ..."
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Abstract. We present a new, onthefly algorithm that, given a pushdown system model representing a sequential program with (recursive) procedure calls and an extended finitestate automaton representing (the negation of) a safety property, produces a succinct, symbolic representation of all counterexamples, i.e., traces of system behaviors that violate the property. The class of what we call minimumrecursion loopfree counterexamples can then be generated from this representation on an asneeded basis and presented to the user. Our algorithm is also applicable, without modification, to finitestate system models. Simultaneous consideration of multiple counterexamples can minimize the number of model checking runs needed to recognize common root causes of property violations. We illustrate the use of our techniques via application to a JavaTar utility and an FTPserver program, and discuss a prototype tool implementation which offers several abstraction techniques for easyviewing of generated counterexamples. 1
Timed relational abstractions for sampled data control systems. Submitted, Under review. 6 Supplementary Material Proof. (Proof sketch for Proposition 1) First, let p(x) be the linear expression c T y + d T z + e discovered in Step (6). Then, dp dt = cT (
 in Step (11). Let p1, p2 be as defined in Step (10). Then, d(p 2 1 + p 2 2) dt = 2p1(αp1 − βp2) + 2p2(βp1 + αp2) = 2α(p 2 1 + p 2 2) Hence, p1(x(t)) 2 + p2(x(t)) 2 = (p1(x(0)) 2 + p2(x(0)) 2 )e 2αt , and therefore, the relation
"... Abstract. In this paper, we define timed relational abstractions for verifying sampled data control systems. Sampled data control systems consist of a plant, modeled as a hybrid system and a synchronous controller, modeled as a discrete transition system. The controller performs control actions on t ..."
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Abstract. In this paper, we define timed relational abstractions for verifying sampled data control systems. Sampled data control systems consist of a plant, modeled as a hybrid system and a synchronous controller, modeled as a discrete transition system. The controller performs control actions on the plant by periodically sampling the state of the plant. The correctness of the system depends on the controller design as well as an appropriate choice of its sampling period. Our approach constructs a timed relational abstraction of the hybrid plant by replacing the continuous plant dynamics by relations. These relations map a state of the plant to states reachable within the sampling time period. We present techniques for building timed relational abstractions, while taking care of discrete transitions that can be taken by the plant between samples. The resulting abstractions are better suited for the verification of sampled data control systems. The abstractions focus on the states that can be observed by the controller at the sample times, while abstracting away behaviors between sample times conservatively. As the abstractions are discrete, infinitestate transition systems, conventional verification tools can be used. We use kinduction to prove safety properties and bounded model checking (BMC) to find potential falsifications. We present our idea, its implementation and results on many benchmark examples. 1
Modeling and analysis of hybrid systems
, 2003
"... First, and foremost, I want to thank my advisor Professor Rajeev Alur. His knowledge and constant guidance have helped me a long way towards completing this thesis. I would also like to thank Professor Insup Lee for chairing my thesis committee, and Professors Vijay Kumar, George Pappas, and Bruce ..."
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First, and foremost, I want to thank my advisor Professor Rajeev Alur. His knowledge and constant guidance have helped me a long way towards completing this thesis. I would also like to thank Professor Insup Lee for chairing my thesis committee, and Professors Vijay Kumar, George Pappas, and Bruce Krogh from the CarnegieMellon University for accepting to be members on my thesis committee. Many thanks go out to Professor Oleg Sokolsky as well. In addition, I would like to thank the whole CIS department for making Penn such a fruitful experience to me. Special thanks go out to Mike Felker who was always helpful. During my time at Penn, I have collaborated with many researchers from the CIS department, as well as other departments of Penn, but also with members of other research organizations. Most importantly, I would like to thank Thao Dang, without whom most of this work would not have been implementable, and who also became a very close friend of mine in the process. Additionally, I would like to thank Eric Aaron, Calin Belta, Ansgar Fehnker, and Jesung Kim for various contributions to my research that is presented in this thesis. I also want to thank Maria Adamou, Dimos
Finding Errors of Hybrid Systems by Optimising an AbstractionBased Quality Estimate
, 2009
"... We present an algorithm for falsifying safety properties of hybrid systems, i.e., for finding a trajectory to an unsafe state. The approach is to approximate how close a point is to being an initial point of an error trajectory using a realvalued quality function, and then to use numerical optimis ..."
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Cited by 4 (3 self)
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We present an algorithm for falsifying safety properties of hybrid systems, i.e., for finding a trajectory to an unsafe state. The approach is to approximate how close a point is to being an initial point of an error trajectory using a realvalued quality function, and then to use numerical optimisation to search for an optimum of this function. The function is computed by running simulations, where information coming from abstractions computed by a verification algorithm is exploited to determine whether a simulation looks promising and should be continued or cancelled. This information becomes more reliable as the abstraction becomes more refined. We thus interleave falsification and verification attempts.
Hybrid automatabased cegar for rectangular hybrid automata
 In http://www.its.caltech.edu/ pavithra/Papers/rtss2012tr.pdf
"... Abstract. In this paper we present a framework for carrying out counterexample guided abstractionrefinement (CEGAR) for systems modelled as rectangular hybrid automata. The main difference, between our approach and previous proposals for CEGAR for hybrid automata, is that we consider the abstract ..."
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Abstract. In this paper we present a framework for carrying out counterexample guided abstractionrefinement (CEGAR) for systems modelled as rectangular hybrid automata. The main difference, between our approach and previous proposals for CEGAR for hybrid automata, is that we consider the abstractions to be hybrid automata as well. We show that the CEGAR scheme is semicomplete for the class of rectangular hybrid automata and complete for the subclass of initialized rectangular automata. We have implemented the CEGAR based algorithm in a tool called Hare, that makes calls to HyTech to analyze the abstract models and validate the counterexamples. Our experiments demonstrate the usefulness of the approach. 1
M.: Preorders for reasoning about stability
 In: HSCC’12
, 2012
"... Preorders between processes, like simulation, have played a central role in the verification and analysis of discretestate systems. Logical characterization of such preorders have allowed one to verify the correctness of a system by analyzing an abstraction of the system. In this paper, we invest ..."
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Preorders between processes, like simulation, have played a central role in the verification and analysis of discretestate systems. Logical characterization of such preorders have allowed one to verify the correctness of a system by analyzing an abstraction of the system. In this paper, we investigate whether this approach can be feasibly applied to reason about stability properties of a system. Stability is an important property of systems that have a continuous component in their state space; it stipulates that when a system is started somewhere close to its ideal starting state, its behavior is close to its ideal, desired behavior. In [6], it was shown that stability with respect to equilibrium states is not preserved by bisimulation and hence additional continuity constraints were imposed on the bisimulation re