N. Halbwachs, P. Raymond, and Y.-E. Proy. Verification of linear hybrid systems by means of convex approximations. In Static Analysis Symposium, number 864 in Lecture Notes in Computer Science, pages 223--237, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....count for each summary node that keeps track of the number of concrete heap nodes represented by the corresponding summary node. 2) Verification with arithmetic constraint manipulation: Arithmetic constraints represented as polyhedra have been used in analyzing real time and concurrent systems [AHH96,BGP99,HRP94]. The techniques we use for integer constraint manipulation are based on [CH78] and [BGP99] 3) Model checking with composite representations: Our earlier work on composite representations concentrated on using BDDs and polyhedral representations together as a symbolic representation to verify ....

N. Halbwachs, P. Raymond, and Y. Proy. Verification of linear hybrid systems by means of convex approximations. In B. LeCharlier, editor, Proceedings of International Symposium on Static Analysis, volume 864 of Lecture Notes in Computer Science. Springer-Verlag, September 1994.

....the concrete transition system of Figure 2 is a possible way to overcome the complexity problems induced by large or infinite state spaces. Notice that for this simple example, having only integer variables with the and operation, we could use tools using polyhedra representations [HPR94] to directly compute the set of reachable states. On the other hand, we know that the deductive approach generates only decidable verification conditions. The key elements are: 1. Defining a set of abstract states and a mapping from concrete to abstract states 2. construct an abstract ....

N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In International Static Analysis Symposium, SAS'94, Namur (Belgium), September 1994.

....scale well with the integer width. This is due to the fact that BDD symbolic representations are specialized for encoding boolean variables and become inefficient when used to represent integer constraints. In stead we can use infinite state representations based on linear arithmetic constraints [1, 3, 16] to solve this problem. Action Language Verifier [2] based upon Composite Symbolic Library [31] that manipulates both BDD and Presburger package, is such an infinite state symbolic model checker. Action Language specifications are modular, each module is defined as a composition of its actions ....

N. Halbwachs, P. Raymond, and Y. Proy. Verification of linear hybrid systems by means of convex approximations. In B. LeCharlier, editor, Proceedings of International Symposium on Static Analysis, volume 864 of Lecture Notes in Computer Science. Springer-Verlag, September 1994.

....system, that is, a constraint system where a further finite set of linear strict inequality constraints is allowed to occur. The usual approach for implementing NNC polyhedra is to embed them into closed polyhedra in a vector space with one extra dimension. While this idea, originally proposed in [7] and also described in [8] proved to be quite e#ective, its direct application results in a low level user interface where most of the geometric intuition of the DD method gets lost under the implementation details . A much cleaner approach was proposed in [1, 2] where the concept of ....

....of an extended generator system, namely, a triple of finite sets containing rays, points and closure points of the polyhedron. By combining the mixed constraint systems with these extended generator systems for describing NNC polyhedra we can obtain a two fold improvement over the proposal in [7, 8]: easier generalizations and a natural, implementation independent interface. Easier generalizations. Several complex operators, whose definition is in terms of the rays and points of the standard generator systems for closed polyhedra, need to be generalized to NNC polyhedra. Examples are given ....

[Article contains additional citation context not shown here]

N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: 15 Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

....and is natural for the specification of embedded systems. Inspired by the success of model checking in hardware verification and protocol analysis [23, 44] there has been increasing research on developing algorithms and tools for automated verification of hybrid models of embedded controllers [1, 6, 7, 10, 17, 32, 40, 41, 15, 51, 55]. Model checking requires the computation of the set of reachable states of a model, and in presence of continuous dynamics, this is typically undecidable. The state of the art computational tools for model checking of hybrid systems are of two kinds. Tools such as Kronos [32] Uppaal [15] and ....

N. Halbwachs, Y. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In International Symposium on Static Analysis, LNCS 864. Springer-Verlag, 1994.

....assumes a specific probability distribution on the inputs. In our on going work, we have modeled and proved some of the policies using a hybrid automaton based model checker HyTech [8] which can model the power dissipation as an analog variable, and the model checking uses polyhedral techniques [7] to handle such analog variables. We also have modeled a probabilistic power management policy using a probabilistic modeling framework, called PRISM [12] Wewill report the results of these modeling and verification activities in a future paper. 5. Acknowledgement This work was supported by ....

N. Halbwachs, P. Raymond, and Y. E. Proy. Verification of linear hybrid systems by means of convex approximation. In Proceedings of the SAS94: Static Analysis Symposium, LNCS 864, pages 223-- 237, 1994.

....detection, loop invariant computations and loop induction variables. Convex polyhedra are also used, among many other applications, for the analysis and verification of synchronous languages [7, 19] and of linear hybrid automata (an extension of finite state machines that models time requirements) [21, 23], for the computer aided formal verification of concurrent and reactive systems based on temporal specifications [28] for inferring argument size relationships in logic languages [5] and for the automatic parallelization of imperative programs [31] Since the work of Cousot and Halbwachs, convex ....

....4 detect some errors, print an error message and abort. Library 2 detects more errors, sometimes setting a flag and sometimes printing a message and aborting. A somewhat drastic approach to error recovery is taken by STeP, the Stanford Temporal Prover [28] STeP uses the Polka polyhedra library [21] by Halbwachs and Y. E. Proy for the automatic generation of invariants. The manual for the latest released version of STeP [8] specifies that this facility is in an experimental state and run as an external process, completely independent from the STeP environment. The user can set three ....

[Article contains additional citation context not shown here]

N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

....detection, loop invariant computations and loop induction variables. Convex polyhedra are also used, among many other applications, for the analysis and verification of synchronous languages [6, 23] and of linear hybrid automata (an extension of finite state machines that models time requirements) [24, 27], for the computer aided formal verification of concurrent and reactive systems based on temporal specifications [29] for inferring argument size relationships in logic languages [4, 5] for the automatic parallelization of imperative programs [31] for detecting bu#er overflows in C [21] and ....

N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

....system, that is, a constraint system where a further finite set of linear strict inequality constraints is allowed to occur. The usual approach for implementing NNC polyhedra is to embed them into closed polyhedra in a vector space with one extra dimension. While this idea, originally proposed in [6] and also described in [7] proved to be quite e#ective, its direct application results in a low level user interface where most of the geometric intuition of the DD method gets lost under the implementation details . A much cleaner approach was proposed in [1, 2] where the concept of generator ....

....type systems and control flow analysis and Aggregate and number reasoning for computing: from decision algorithms to constraint programming with multisets, sets, and maps . The use of closure points in the approach proposed in [1, 2] provides a twofold improvement over the proposal in [6, 7]: first, an NNC polyhedron can be presented to the client application directly in terms of its defining strict and non strict constraints or its generating rays, points and closure points; second, the implementation becomes separate from the user interface. In this paper we exploit the latter ....

[Article contains additional citation context not shown here]

N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

....system, that is, a constraint system where a further finite set of linear strict inequality constraints is allowed to occur. The usual approach for implementing NNC polyhedra is to embed them into closed polyhedra in a vector space with one extra dimension. While this idea, originally proposed in [6] and also described in [7] proved to be quite e#ective, its direct application results in a low level user interface where most of the geometric intuition of the DD method gets lost under the implementation details . A much cleaner approach was proposed in [1, 2] where the concept of generator ....

....type systems and control flow analysis and Aggregate and number reasoning for computing: from decision algorithms to constraint programming with multisets, sets, and maps . The use of closure points in the approach proposed in [1, 2] provides a twofold improvement over the proposal in [6, 7]: first, an NNC polyhedron can be presented to the client application directly in terms of its defining strict and non strict constraints or its generating rays, points and closure points; second, the implementation becomes separate from the user interface. In this paper we exploit the latter ....

[Article contains additional citation context not shown here]

N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

....Model checking. Inspired by the success of model checking in hardware verification and protocol analysis [24] 25] there has been increasing research on developing techniques for automated verification of hybrid (mixed discretecontinuous) models of embedded controllers [13] 26] 27] [28], 29] The state of the art computational tools for model checking of hybrid systems are of two kinds. Tools such as KRONOS [30] UPPAAL [31] and HYTECH [32] limit the continuous dynamics to simple abstractions such as rectangular inclusions (e.g. 1,2] and compute the set of reachable states ....

N. Halbwachs, Y. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In International Symposium on Static Analysis, LNCS 864, 1994.

....and Aggregate and number reasoning for computing: from decision algorithms to constraint programming with multisets, sets, and maps and by EPSRC grant GR R53401 01. synchronous languages [6, 18] and of linear hybrid automata (an extension of finite state machines that models time requirements) [20, 22], for the computeraided formal verification of concurrent and reactive systems based on temporal specifications [27] for inferring argument size relationships in logic languages [5] and for the automatic parallelization of imperative programs [30] Since the work of Cousot and Halbwachs, convex ....

....have (note that if and only if n = 0) When partially ordered by set inclusion, is a lattice and is a sublattice of . To the best of the authors knowledge, the first software library (based on the DD method) allowing for the computation over the domain was the Polka library [20], where each NNC polyhedron is embedded into a closed . The additional dimension of the vector space, usually labeled by the letter #, encodes the topological closeness of each a#ne half space in the constraint description for . Namely, if = con(C) where i , x# ## i b i . ....

[Article contains additional citation context not shown here]

N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

....for vehicle coordination. 1 Introduction Inspired by the success of model checking in hardware verification and proto col analysis [8, 17] there has been increasing research on developing techniques for automated verification of hybrid (mixed discrete continuous) models of embedded controllers [1, 3, 15]. The state of the art computational tools for model checking of hybrid systems are of two kinds. Tools such as KRONOS [11] UPP L [20] and HYTECH [16] limit the continuous dynamics to simple abstractions such as rectangular inclusions (e.g. 1,2] and compute the set of reachable states ....

N. Halbwachs, Y. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In Intern. Symposium on Static Analysis, LNCS

....time has to be fixed a priori [Alu91] Dense real time models are decidable (for certain syntactic restrictions) and model checking algorithms can be formulated [ACD93] In the recent years a number of tools have been developed on this background. To name a few of them: Epsilon [CGL93] Polka [HRP94] Rt Cospan [AK95] Rt Spin [TC96] Treat [KL96] Kronos [BDM 98] Uppaal [LPY97] HyTech [HHWT97] CMC [LL98] and SGM [WH98] All of them originate from academic environments. For dense real time the state space is generally infinite; the decidability results depend on the fact that it ....

Nicolas Halbwachs, Pascal Raymond, and Yann-Erick Proy. Verification of Linear Hybrid Systems by Means of Convex Approximations. In Static Analysis Symposium, volume 864 of Lecture Notes in Computer Science (LNCS), pages 223--237, 1994. 76

....predicate abstraction. Inspired by the success of model checking in hardware verification and protocol analysis [21] 46] there has been increasing research on developing techniques for automated verification of hybrid (mixed discrete continuous) models of embedded controllers [1] 3] 6] [40], 42] The state of the art computational tools for model checking of hybrid sys tems are of two kinds. Tools such as KRONOS [28] UPPAAL [51] and HYTECH [43] limit the continuous dynam ics to simple abstractions such as rectangular inclusions (e.g. 1, 2] and compute the set of reachable ....

N. Halbwachs, Y. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In International Symposium on Static Analysis, LNCS 864, 1994.

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N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Proc. of the 1st Int. Static Analysis Symposium, LNCS 864, pages 223--237. Springer, 1994.

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N. Halbwachs, P. Raymond, and Y.-E. Proy. Verification of linear hybrid systems by means of convex approximations. In Static Analysis Symposium, number 864 in Lecture Notes in Computer Science, pages 223--237, 1994.

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N. Halbwachs, Y.-E. Proy, P. Raymond, Verification of linear hybrid systems by means of convex approximations, in: B. Le Charlier (Ed.), Static Analysis: 31 Proceedings of the 1st International Symposium, Vol. 864 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Namur, Belgium, 1994, pp. 223--237.

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N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

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N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

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N. Halbwachs, Y.-E. Proy, P. Raymond, Verification of linear hybrid systems by means of convex approximations, in: B. Le Charlier (Ed.), Static Analysis: 31 Proceedings of the 1st International Symposium, Vol. 864 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Namur, Belgium, 1994, pp. 223--237.

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N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

No context found.

N. Halbwachs, Y.-E. Proy, and P. Raymond. Verification of linear hybrid systems by means of convex approximations. In B. Le Charlier, editor, Static Analysis: Proceedings of the 1st International Symposium, volume 864 of Lecture Notes in Computer Science, pages 223--237, Namur, Belgium, 1994. Springer-Verlag, Berlin.

No context found.

N. Halbwachs, P. Raymond, and Y. Proy. Verification of linear hybrid systems by means of convex approximations. In B. LeCharlier, editor, Proceedings of International Symposium on Static Analysis, volume 864 of Lecture Notes in Computer Science. Springer-Verlag, September 1994.

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N. Halbwachs, Y. Proy, and P. Raymond, "Verification of linear hybrid systems by means of convex approximations," in Lecture Notes in Computer Science, Static Analysis. Heidelberg, Germany: Springer-Verlag, 1994, vol. 864.

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