J. Mller, J. Lichtenberg, H. Andersen, and H. Hulgaard, Difference Decision Diagrams, Proc. CSL'99, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....5 is dedicated to the description of the solver, while some preliminary experimental results are described in Section 6. We conclude with some related work. 2 Difference Logic In this section we define the class of formulae that we consider. This class has already been used elsewhere (see e.g. MLAH99,LPWY99,ABK 97,BM00,ACG99] and is probably part of folklore, but to give it a name let us call it difference logic (DL) We use two slightly different variants, DLZ and DLR depending on the domain of the numerical variables. Definition 1 (Difference Logic) Let B 1 , B 2 , be a ....

J. Mller, J. Lichtenberg, H. Andersen, and H. Hulgaard, Difference Decision Diagrams, Proc. CSL'99, 1999.

....x; y 1) The set Z ; is f j (x) 3 or (y) 2g, which is not a zone (non convex) x 3; a; x : 0 y : 0 y 2; a; x : 0 y : 0 Location Dependent Maximal Constants. Even with a suitable representation of the closed sets (e.g. using lists of zones or structures as CDDs [4] DDDs [21]) the actual computation of the closure would be at least as difficult as solving the locationreachability problem itself [1, 2] What we are looking for is an alternative abstraction obtained by a more efficient analysis of the relevance of guards. The method proposed in the following determines ....

J. Mller, J. Lichtenberg, H.R. Andersen, and H. Hulgaard. Difference Decision Diagrams. In Proc. 13th Int. Workshop on Computer Science Logic (CSL'99), vol. 1683 of LNCS, pp. 111--125. Springer, 1999. 16

....In Section 5 the overall procedure and tool architecture is explained along with remarks on the first experiments with our running prototype. 2 Difference Logic In this section we define formally the class of formulae that we consider. This class has already been used elsewhere (see e.g. MLAH99,LPWY99,ABK 97,BM00] and is probably part of folklore, but to give it a name let us call it difference logic (DL) We use two slightly different variants, DLZ and DLR depending on the domain of the numerical variables. Definition 1 (Difference Logic) Let B 1 , B 2 , be a set of ....

J. Mller, J. Lichtenberg, H. Andersen, and H. Hulgaard. Difference decision diagrams. In Proc. CSL'99, 1999.

....the symbolic state space which are guaranteed not to contain optimal solutions. In particular, by introducing an additional clock for accumulating time elapses, the minimum time reachability problem may be dealt with using the existing e#cient data structures (e.g. DBMs [60] CDDs [110] and DDDs [123]) already used in the realtime verification tools Uppaal and Kronos for reachability. The results of the present paper also extends the work in [10] which provides an algorithm for computing the accumulated delay in a timed automata. In this paper, we provide the basis for dealing with more ....

J. Mller, J. Lichtenberg, H. R. Andersen, and H. Hulgaard. Difference decision diagrams. Technical Report IT-TR-

....includes studying other symbolic representations and associated extrapolation techniques, and identifying classes of arithmetical constraints that can be handled efficiently. In particular, it would be interesting to investigate parametric extensions of structures like CDD s [LPWY99] and DDD s [MLAH99] Finally, let us mention that in this paper we have addressed only forward reachability analysis. Actually, the techniques we have developed can also be used for backward analysis as well. ....

J. Moller, J. Lichtenberg, H.R. Andersen, and H. Hulgaard. Difference decision diagrams. Tech. rep it-tr-

....over all unfoldings. Hulgaard and Burns[36] 11] also extended this work to systems with certain types of choices. Recently, symbolic timing verification has been studied by Amon et al. 37] 38] Timing verification using difference decision diagrams has also been attempted by Mller et al. [39]. All of these techniques, however, have worst case complexity that is at least exponential in the size of the system description. IV. ANALYZING ACYCLIC GRAPHS In this section, we develop a polynomial time algorithm for computing approximate bounds on time separations of all pairs of events in an ....

J. Mller, J. Lichtenberg, H. R. Andersen, and H. Hulgaard, "Difference decision diagrams," Tech. Rep. IT-TR-1999-023, Department of Information Technology, Technical University of Denmark, 1999.

....canonical form, the so called reduced ordered BDD (ROBDD) After canonical forms have been established equivalence checking and satisfiability testing are trivial. Constructing the canonical form however, can be exponential. Various extensions to the basic data type have been proposed, like DDDs [9], BEDs [1] and EQ BDDs [6] Many variants of Bryant s original apply algorithm for computing boolean combinations of ROBDDs have been proposed in the literature. Usually, such adaptations are motivated by particular benchmarks, that show a speed up for certain cases. In many cases, the relative ....

Mller, J., Lichtenberg, J., Andersen, H. R., and Hulgaard, H. Difference decision diagrams. In Computer Science Logic (Denmark, Sept. 1999).

.... Project 26270 VHS (Verification of Hybrid systems) and the French Israeli collaboration project 970maefut5 (Hybrid Models of Industrial Plants) Consequently, the search for new representation schemes for timed polyhedra is a very active domain of research [ABK 97] BMPY97] S99] MLAH99b] BLP 99] W00] In this paper, we propose a new representation scheme for non convex timed polyhedra based on a reformulation and extension of our previous work in [BMP99] where we proposed a canonical representation for non convex orthogonal polyhedra. As in [BMP99] the representation is ....

J. Mller, J. Lichtenberg, H.R. Andersen, and H. Hulgaard, Difference Decision Diagrams, Proc. CSL'99, 1999.

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