In this paper we discuss the problem of calculating the reachable states of a dynamical system de... more In this paper we discuss the problem of calculating the reachable states of a dynamical system defined by ordinary differential equations or inclusions. We present a prototype system for approximating this set and demonstrate some experimental results.
Predicate abstraction has emerged to be a powerful technique for extracting finite-state models f... more Predicate abstraction has emerged to be a powerful technique for extracting finite-state models from infinite-state discrete programs. Th is paper presents algorithms and tools for reachability analysis of hybrid systems by combining the notion of predicate abstraction with recent techniques for approximating the set of reachable states of linear systems using polyhedra.Giv en a hybrid system and a set of userde fined boolean predicates, we consider the finite discrete quotient whose states correspond to all possible truth assignments to the input predicates. T he tool performs an on-the-fly exploration of the abstract system. We demonstrate the feasibility of the proposed technique by analyzing a parametric timing-based mutual exclusion protocol and safety of a simple controller for vehicle coordination.
In this article, we describe some recent results on the hybridization methods for the analysis of... more In this article, we describe some recent results on the hybridization methods for the analysis of nonlinear systems. The main idea of our hybridization approach is to apply the hybrid systems methodology as a systematic approximation method. More concretely, we partition the state space of a complex system into regions that only intersect on their boundaries, and then approximate its dynamics in each region by a simpler one. Then, the resulting hybrid system, which we call a hybridization, is used to yield approximate analysis results for the original system. We also prove important properties of the hybridization, and propose two effective hybridization construction methods, which allow approximating the original nonlinear system with a good convergence rate.
In this paper we present an approach to approximate reachability computation for nonlinear contin... more In this paper we present an approach to approximate reachability computation for nonlinear continuous systems. Rather than studying a complex nonlinear system x = g(x), we study an approximating system x = f(x) which is easier to handle. The class of approximating systems we consider in this paper is piecewise linear, obtained by interpolating g over a mesh. In order to be conservative, we add a bounded input in the approximating system to account for the interpolation error. We thus develop a reachability method for systems with input, based on the relation between such systems and the corresponding autonomous systems in terms of reachable sets. This method is then extended to the approximate piecewise linear systems arising in our construction. The final result is a reachability algorithm for nonlinear continuous systems which allows to compute conservative approximations with as great degree of accuracy as desired, and more importantly, it has good convergence rate. If g is a C 2 function, our method is of order 2. Furthermore, the method can be straightforwardly extended to hybrid systems.
This paper describes the modeling language Charon for modular design of interacting hybrid system... more This paper describes the modeling language Charon for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy, and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools, and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of Charon in design of embedded control software using examples from automated highways concerning vehicle coordination.
Predicate abstraction has emerged to be a powerful technique for extracting finite-state models f... more Predicate abstraction has emerged to be a powerful technique for extracting finite-state models from infinite-state systems, and has been recently shown to enhance the effectiveness of the reachability computation techniques for hybrid systems. Given a hybrid system with linear dynamics and a set of linear predicates, the verifier performs an on-the-fly search of the finite discrete quotient whose states correspond to the truth assignments to the input predicates. To compute the transitions out of an abstract state, the tool needs to compute the set of discrete and continuous successors, and find out all the abstract states that this set intersects with. The complexity of this computation grows exponentially with the number of abstraction predicates. In this paper we present various optimizations that are aimed at speeding up the search in the abstract state-space, and demonstrate their benefits via case studies. We also discuss the completeness of the predicate abstraction technique for proving safety of hybrid systems.
Silicon based technology will reach its limits in 2020 when the channel length of MOSFET is below... more Silicon based technology will reach its limits in 2020 when the channel length of MOSFET is below 10nm. For this reason, the semiconductor industry is looking for different materials and devices to integrate with the current silicon-based technology or maybe, in a long term ...
In this paper we discuss the problem of calculating the reachable states of a dynamical system de... more In this paper we discuss the problem of calculating the reachable states of a dynamical system defined by ordinary differential equations or inclusions. We present a prototype system for approximating this set and demonstrate some experimental results.
Predicate abstraction has emerged to be a powerful technique for extracting finite-state models f... more Predicate abstraction has emerged to be a powerful technique for extracting finite-state models from infinite-state discrete programs. Th is paper presents algorithms and tools for reachability analysis of hybrid systems by combining the notion of predicate abstraction with recent techniques for approximating the set of reachable states of linear systems using polyhedra.Giv en a hybrid system and a set of userde fined boolean predicates, we consider the finite discrete quotient whose states correspond to all possible truth assignments to the input predicates. T he tool performs an on-the-fly exploration of the abstract system. We demonstrate the feasibility of the proposed technique by analyzing a parametric timing-based mutual exclusion protocol and safety of a simple controller for vehicle coordination.
In this article, we describe some recent results on the hybridization methods for the analysis of... more In this article, we describe some recent results on the hybridization methods for the analysis of nonlinear systems. The main idea of our hybridization approach is to apply the hybrid systems methodology as a systematic approximation method. More concretely, we partition the state space of a complex system into regions that only intersect on their boundaries, and then approximate its dynamics in each region by a simpler one. Then, the resulting hybrid system, which we call a hybridization, is used to yield approximate analysis results for the original system. We also prove important properties of the hybridization, and propose two effective hybridization construction methods, which allow approximating the original nonlinear system with a good convergence rate.
In this paper we present an approach to approximate reachability computation for nonlinear contin... more In this paper we present an approach to approximate reachability computation for nonlinear continuous systems. Rather than studying a complex nonlinear system x = g(x), we study an approximating system x = f(x) which is easier to handle. The class of approximating systems we consider in this paper is piecewise linear, obtained by interpolating g over a mesh. In order to be conservative, we add a bounded input in the approximating system to account for the interpolation error. We thus develop a reachability method for systems with input, based on the relation between such systems and the corresponding autonomous systems in terms of reachable sets. This method is then extended to the approximate piecewise linear systems arising in our construction. The final result is a reachability algorithm for nonlinear continuous systems which allows to compute conservative approximations with as great degree of accuracy as desired, and more importantly, it has good convergence rate. If g is a C 2 function, our method is of order 2. Furthermore, the method can be straightforwardly extended to hybrid systems.
This paper describes the modeling language Charon for modular design of interacting hybrid system... more This paper describes the modeling language Charon for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy, and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools, and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of Charon in design of embedded control software using examples from automated highways concerning vehicle coordination.
Predicate abstraction has emerged to be a powerful technique for extracting finite-state models f... more Predicate abstraction has emerged to be a powerful technique for extracting finite-state models from infinite-state systems, and has been recently shown to enhance the effectiveness of the reachability computation techniques for hybrid systems. Given a hybrid system with linear dynamics and a set of linear predicates, the verifier performs an on-the-fly search of the finite discrete quotient whose states correspond to the truth assignments to the input predicates. To compute the transitions out of an abstract state, the tool needs to compute the set of discrete and continuous successors, and find out all the abstract states that this set intersects with. The complexity of this computation grows exponentially with the number of abstraction predicates. In this paper we present various optimizations that are aimed at speeding up the search in the abstract state-space, and demonstrate their benefits via case studies. We also discuss the completeness of the predicate abstraction technique for proving safety of hybrid systems.
Silicon based technology will reach its limits in 2020 when the channel length of MOSFET is below... more Silicon based technology will reach its limits in 2020 when the channel length of MOSFET is below 10nm. For this reason, the semiconductor industry is looking for different materials and devices to integrate with the current silicon-based technology or maybe, in a long term ...
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