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120,353
Symbolic Reachability Computation for Families of Linear Vector Fields
 Journal of Symbolic Computation
, 2001
"... this paper, we present the first known families of linear di#erential equations with a decidable reachability problem. This is achieved by posing the reachability computation as a quantifier elimination problem in the decidable theory of the reals. We illustrate the applicability of our approach by ..."
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Cited by 92 (4 self)
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this paper, we present the first known families of linear di#erential equations with a decidable reachability problem. This is achieved by posing the reachability computation as a quantifier elimination problem in the decidable theory of the reals. We illustrate the applicability of our approach
Approximate reachability computation for polynomial systems
 in HSCC’06, vol. 3927 in LNCS
, 2006
"... Abstract. In this paper we propose an algorithm for approximating the reachable sets of systems defined by polynomial differential equations. Such systems can be used to model a variety of physical phenomena. We first derive an integration scheme that approximates the state reachable in one time ste ..."
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Cited by 19 (10 self)
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step by applying some polynomial map to the current state. In order to use this scheme to compute all the states reachable by the system starting from some initial set, we then consider the problem of computing the image of a set by a multivariate polynomial. We propose a method to do so using
Reachability Computation For Linear Hybrid Systems
 In Proceedings of the 14th IFAC World Congress, volume E
, 1998
"... : Linear hybrid systems are finite state machines with linear vector fields of the form x = Ax in each discrete location. Very recently, the reachability problem for classes of linear hybrid systems was shown to be decidable. In this paper, the decidability result is extended to capture classes of ..."
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Cited by 13 (3 self)
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for hybrid systems is the reachability problem which asks whether some unsafe region is reachable from an initial region. The reachability problem for hybrid systems is known to be difficult. In order to tackle the complexity of the reachability problem, we adopt a computational point of view. The important
Reachability computation for hybrid systems with Ariadne
 In Proc. the 17th IFAC World Congress
, 2008
"... Abstract: Ariadne is an inprogress open environment to design algorithms for computing with hybrid automata, that relies on a rigorous computable analysis theory to represent geometric objects, in order to achieve provable approximation bounds along the computations. In this paper we discuss the pr ..."
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Cited by 6 (1 self)
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the problem of reachability analysis of hybrid automata to decide safety properties. We describe in details the algorithm used in Ariadne to compute overapproximations of reachable sets. Then we show how it works on a simple example. Finally, we discuss the lowerapproximation approach to the reachability
Using counterexamples for improving the precision of reachability computation with polyhedra
 in Computer Aided Verification (CAV’07
, 2007
"... Abstract. We present an extrapolation with care set operator to accelerate termination of reachability computation with polyhedra. At the same time, a counterexample guided refinement algorithm is used to iteratively expand the care set to improve the precision of the reachability computation. We al ..."
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Cited by 12 (1 self)
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Abstract. We present an extrapolation with care set operator to accelerate termination of reachability computation with polyhedra. At the same time, a counterexample guided refinement algorithm is used to iteratively expand the care set to improve the precision of the reachability computation. We
Distanceconstraint reachability computation in uncertain graphs
 PVLDB
"... Driven by the emerging network applications, querying and mining uncertain graphs has become increasingly important. In this paper, we investigate a fundamental problem concerning uncertain graphs, which we call the distanceconstraint reachability (DCR) problem: Given two vertices s and t, what is ..."
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Cited by 25 (5 self)
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Driven by the emerging network applications, querying and mining uncertain graphs has become increasingly important. In this paper, we investigate a fundamental problem concerning uncertain graphs, which we call the distanceconstraint reachability (DCR) problem: Given two vertices s and t, what
Interprocedural dataflow analysis via graph reachability
, 1994
"... The paper shows how a large class of interprocedural dataflowanalysis problems can be solved precisely in polynomial time by transforming them into a special kind of graphreachability problem. The only restrictions are that the set of dataflow facts must be a finite set, and that the dataflow fun ..."
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Cited by 454 (34 self)
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The paper shows how a large class of interprocedural dataflowanalysis problems can be solved precisely in polynomial time by transforming them into a special kind of graphreachability problem. The only restrictions are that the set of dataflow facts must be a finite set, and that the dataflow
NLTOOLBOX: A library for reachability computation of nonlinear dynamical systems
"... Abstract. We describe NLTOOLBOX, a library of data structures and algorithms for reachability computation of nonlinear dynamical systems. It provides the users with an easy way to ”program ” their own analysis procedures or to solve other problems beyond verification. We illustrate the use of the li ..."
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Cited by 2 (0 self)
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Abstract. We describe NLTOOLBOX, a library of data structures and algorithms for reachability computation of nonlinear dynamical systems. It provides the users with an easy way to ”program ” their own analysis procedures or to solve other problems beyond verification. We illustrate the use
A Geometric Approach To Reachability Computations For Constrained DiscreteTime Systems
 IN PROCEEDINGS OF THE 15TH IFAC WORLD CONGRESS ON AUTOMATIC CONTROL
, 2002
"... The problem of reachability computations for systems with simultaneous constraints on the states, control inputs and disturbances is treated. A problem formulation is provided for the general case and, for the special case where the disturbance constraints are independent of the states and inputs ..."
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Cited by 4 (3 self)
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The problem of reachability computations for systems with simultaneous constraints on the states, control inputs and disturbances is treated. A problem formulation is provided for the general case and, for the special case where the disturbance constraints are independent of the states
Reachability Analysis of Pushdown Automata: Application to ModelChecking
, 1997
"... We apply the symbolic analysis principle to pushdown systems. We represent (possibly infinite) sets of configurations of such systems by means of finitestate automata. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification (like mode ..."
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Cited by 385 (39 self)
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modelchecking for branchingtime logics), we consider the more general class of alternating pushdown systems and use alternating finitestate automata as a representation structure for their sets of configurations. We give a simple and natural procedure to compute sets of predecessors
Results 1  10
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120,353