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41
Symbolic analysis for improving simulation coverage of simulink/stateflow models
 in EMSOFT ’08: Proceedings of the 8th ACM international conference on Embedded software, 2008
"... Aimed at verifying safety properties and improving simulation coverage for hybrid systems models of embedded control software, we propose a technique that combines numerical simulation and symbolic methods for computing statesets. We consider systems with linear dynamics described in the commercial ..."
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Cited by 37 (4 self)
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Aimed at verifying safety properties and improving simulation coverage for hybrid systems models of embedded control software, we propose a technique that combines numerical simulation and symbolic methods for computing statesets. We consider systems with linear dynamics described in the commercial modeling tool Simulink/Stateflow. Given an initial state x, and a discretetime simulation trajectory, our method computes a set of initial states that are guaranteed to be equivalent to x, where two initial states are considered to be equivalent if the resulting simulation trajectories contain the same discrete components at each step of the simulation. We illustrate the benefits of our method on two case studies. One case study is a benchmark proposed in the literature for hybrid systems verification and another is a Simulink demo model from Mathworks.
Formal verification of hybrid systems
, 2011
"... In formal verification, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements. The appropriate mathematical model for embedded control systems is hybrid systems that combines th ..."
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Cited by 34 (0 self)
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In formal verification, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements. The appropriate mathematical model for embedded control systems is hybrid systems that combines the traditional statemachine based models for discrete control with classical differentialequations based models for continuously evolving physical activities. In this article, we briefly review selected existing approaches to formal verification of hybrid systems, along with directions for future research.
Reachability analysis of multiaffine systems
 In Hybrid Systems: Computation and Control, LNCS 3927
, 2006
"... Abstract We present a computationally attractive technique to study the reachability of rectangular regions by trajectories of continuous multiaffine systems. The method is iterative. At each step, finer partitions and finite quotients that overapproximate the reachability properties of the initi ..."
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Cited by 31 (4 self)
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Abstract We present a computationally attractive technique to study the reachability of rectangular regions by trajectories of continuous multiaffine systems. The method is iterative. At each step, finer partitions and finite quotients that overapproximate the reachability properties of the initial system are produced. We exploit some convexity properties of multiaffine functions on rectangles to show that the construction of the quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. This methodology can be used for formal analysis of biochemical networks, aircraft and underwater vehicles, where multiaffine models are widely used.
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 18 (17 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
Synthesis of quantized feedback control software for discrete time linear hybrid systems
, 2010
"... Abstract. We present an algorithm that given a Discrete Time Linear Hybrid System H returns a correctbyconstruction software implementation K for a (near time optimal) robust quantized feedback controller for H along with the set of states on which K is guaranteed to work correctly (controllable ..."
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Cited by 16 (15 self)
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Abstract. We present an algorithm that given a Discrete Time Linear Hybrid System H returns a correctbyconstruction software implementation K for a (near time optimal) robust quantized feedback controller for H along with the set of states on which K is guaranteed to work correctly (controllable region). Furthermore, K has a Worst Case Execution Time linear in the number of bits of the quantization schema. 1
The Complete Proof Theory of Hybrid Systems
, 2011
"... as representing the official policies, either expressed or implied, of any sponsoring institution or government. Keywords: proof theory; hybrid dynamical systems; differential dynamic logic; axiomatization; Hybrid systems are a fusion of continuous dynamical systems and discrete dynamical systems. T ..."
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Cited by 16 (12 self)
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as representing the official policies, either expressed or implied, of any sponsoring institution or government. Keywords: proof theory; hybrid dynamical systems; differential dynamic logic; axiomatization; Hybrid systems are a fusion of continuous dynamical systems and discrete dynamical systems. They freely combine dynamical features from both worlds. For that reason, it has often been claimed that hybrid systems are more challenging than continuous dynamical systems and than discrete systems. We now show that, prooftheoretically, this is not the case. We present a complete prooftheoretical alignment that interreduces the discrete dynamics and continuous dynamics of hybrid systems. We give a sound and complete axiomatization of hybrid systems relative to continuous dynamical systems and a sound and complete axiomatization of hybrid systems relative to discrete dynamical systems. Thanks to our axiomatization, proving properties of hybrid systems is exactly the same as proving properties of continuous dynamical systems and again, exactly the same as proving properties of discrete dynamical systems. This fundamental cornerstone sheds light on the nature of hybridness and enables flexible and provably perfect combinations of discrete reasoning with continuous reasoning that lift to all aspects of hybrid systems and their fragments. 1
Automatic abstraction refinement for timed automata
 In Proc. FORMATS’07, volume 4763 of LNCS
, 2007
"... Abstract. We present a fully automatic approach for counterexample guided abstraction refinement of realtime systems modelled in a subset of timed automata. Our approach is implemented in the MOBY/RT tool environment, which is a CASE tool for embedded system specifications. Verification in MOBY/RT ..."
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Cited by 9 (0 self)
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Abstract. We present a fully automatic approach for counterexample guided abstraction refinement of realtime systems modelled in a subset of timed automata. Our approach is implemented in the MOBY/RT tool environment, which is a CASE tool for embedded system specifications. Verification in MOBY/RT is done by constructing abstractions of the semantics in terms of timed automata which are fed into the model checker UPPAAL. Since the abstractions are overapproximations, absence of abstract counterexamples implies a valid result for counterexample is found by UPPAAL. The generated abstract counterexample is used to construct either a concrete counterexample for the full model or to identify a slightly refined abstraction in which the found spurious counterexample cannot occur anymore. Hence, the approach allows for a fully automatic abstraction refinement loop starting from the coarsest abstraction towards an abstraction for which a valid verification result is found. Nontrivial case studies demonstrate that this approach computes small abstractions fast without any user interaction. 1
E.: Quantized feedback control software synthesis from system level formal specifications
 CoRR
, 2011
"... Many Embedded Systems are indeed Software Based Control Systems (SBCSs), that is control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for automatic synthesis of SBCS control software. ..."
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Cited by 7 (7 self)
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Many Embedded Systems are indeed Software Based Control Systems (SBCSs), that is control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for automatic synthesis of SBCS control software. In previous works we presented an algorithm, along with a tool QKS implementing it, that from a formal model (as a Discrete Time Linear Hybrid System, DTLHS) of the controlled system (plant), implementation specifications (that is, number of bits in the AnalogtoDigital, AD, conversion) and System Level Formal Specifications (that is, safety and liveness requirements for the closed loop system) returns correctbyconstruction control software that has a Worst Case Execution Time (WCET) linear in the number of AD bits and meets the given specifications. In this technical report we present full experimental results on using it to synthesize control software for two versions of buck DCDC converters (singleinput and multiinput), a widely used mixedmode analog circuit. 1 ar
Proof Assistants: history, ideas and future
"... In this paper we will discuss the fundamental ideas behind proof assistants: What are they and what is a proof anyway? We give a short history of the main ideas, emphasizing the way they ensure the correctness of the mathematics formalized. We will also briefly discuss the places where proof assista ..."
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Cited by 7 (0 self)
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In this paper we will discuss the fundamental ideas behind proof assistants: What are they and what is a proof anyway? We give a short history of the main ideas, emphasizing the way they ensure the correctness of the mathematics formalized. We will also briefly discuss the places where proof assistants are used and how we envision their extended use in the future. While being an introduction into the world of proof assistants and the main issues behind them, this paper is also a position paper that pushes the further use of proof assistants. We believe that these systems will become the future of mathematics, where definitions, statements, computations and proofs are all available in a computerized form. An important application is and will be in computer supported modelling and verification of systems. But their is still along road ahead and we will indicate what we believe is needed for the further proliferation of proof assistants.
Discretestate abstractions of nonlinear systems using multiresolution quantizer
 Hybrid Systems: Computation and Control
, 2009
"... Abstract. This paper proposes a design method for discrete abstractions of nonlinear systems using multiresolution quantizer, which is capable of handling state dependent approximation precision requirements. To this aim, we extend the notion of quantizer embedding, which has been proposed by the ..."
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Cited by 6 (1 self)
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Abstract. This paper proposes a design method for discrete abstractions of nonlinear systems using multiresolution quantizer, which is capable of handling state dependent approximation precision requirements. To this aim, we extend the notion of quantizer embedding, which has been proposed by the authors ’ previous works as a transformation from continuousstate systems to discretestate systems, to a multiresolution setting. Then, we propose a computational method that analyzes how a locally generated quantization error is propagated through the state space. Based on this method, we present an algorithm that generates a multiresolution quantizer with a specified error precision by finite refinements. Discrete abstractions produced by the proposed method exhibit nonuniform distribution of discrete states and inputs. 1