D.Dill, \Timing Assumptions and Veri cation of Finite-State Concurrent Systems," Proc.CAV Methods for Finite State Systems, Grenoble, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....version of regions, and is thus guaranteed to be extremely inecient and highly sensitive to the size of constants used in the models. As the rst contribution of this paper, we give for the subclass of UPTA an ef cient zone representation of symbolic cost states based on Di erence Bound Matrices [Dil89] and give all the necessary symbolic operators needed to implement the algorithm. As the second contribution we show that, in analogy with Dijkstra s shortest path algorithm, if the algorithm is modi ed to always Formally C v C i 8u: C (u) C(u) select from Waiting the (symbolic ....

....in Fig. 1 uses symbolic cost states, quite similar to how timed automata model checkers like Uppaal use symbolic states. Typically, symbolic states are pairs on the form (l; Z) where Z R is a convex set of clock valuations, called a zone, representable by Di erence Bound Matrices (DBMs) Dil89] The operations needed for forward state space exploration can be eciently implemented using the DBM data structure. However, the operations might as well be de ned in terms of characteristic functions, R f0; 1g. For example, let be the characteristic function of a zone Z. Then delay can ....

D. Dill, Timing Assumptions and Veri cation of Finite-State Concurrent Systems, Proc. of Automatic Veri cation Methods for Finite State Systems (J. Sifakis, ed.), Lecture Notes in Computer Science, no. 407, Springer{ Verlag, 1989, pp. 197-212.

....inclusion and emptiness. In the computation of the set Next, operations for intersection, forward time projection (future) and projection in one dimension (clock reset) are required. A well known data structure for representing clock constraint systems is that of Di erence Bounded Matrices, DBM, [Dill87], giving for each pair of clocks the upper bound on their di erence. All operations required in the reachability analysis in Figure 1 can be easily implemented on DBM s with satisfactory eciency. In particular, the various operations may bene t from a canonical DBM representation with tightest ....

D.L. Dill. Timing Assumptions and Veri cation of Finite-State Concurrent Systems. in: J. Sifakis (Ed.), Automatic Veri cation Methods for Finite State Systems. LNCS 407, Springer Berlin 1989, pp. 197-212.

....described in section 5. A partial order reduction method is presented in Section 6. The next two sections contain experimental results and conclusions. 2 Related Work Our approach to abstract state spaces of Time Petri Nets improves the one of [YR98] which is a re nement of the method of [BD91,Dil89] As far as we know this approach gives much smaller state spaces than the region graph method of [ACD90] So far partial order reductions have been de ned only for linear time properties either for Time Petri Nets [YS97,Lil99] or for Timed Automata of standard [Pag96,DGKK98] or local semantics ....

....state graph. So, correctness follows again from Theorem 6. 7 Experimental results Our algorithm has been implemented on the base of the program described in [YR98] we have received by courtesy of Tomohiro Yoneda. The sets of inequalities describing state classes are represented by DBM matrices [Dil89] The present implementation does not contain any compressing procedure and therefore should be optimized for practical purposes. A small net is presented in Figure 4. We display the sizes of its (detailed) region graph of [ACD90] taken from [YR98] geometric region, atomic and pseudoatomic ....

D. Dill, Timing Assumptions and Verication of Finite State Concurrent Systems, LNCS 407 (1989), 197 - 212.

....techniques to prune parts of the symbolic statespace which are guaranteed not to contain optimal solutions. In particular, by introducing an additional clock for accumulating time elapses, the minimumtime reachability problem may be dealt with using the existing ecient data structures (e.g. DBMs [Dil89] CDDs [LWYP99] and DDDs [MLAH99] already used in the real time veri cation tools Uppaal and Kronos for reachability. The results of the present paper also extends the work in [ACH93] which provides an algorithm for computing the accumulated delay in a timed automata. In this paper, we provide ....

David Dill, Timing Assumptions and Verication of Finite-State Concurrent Systems, Proc. of Automatic Verication Methods for Finite State Systems (J. Sifakis, ed.), Lecture Notes in Computer Science, no. 407, Springer{Verlag, 1989, pp. 197-212.

....to a new notion, viz. that of the facets of a zone. The suitability of the LPTA model for scheduling problems was already illustrated in [BFH ] using the more restricted Uniformly Priced Timed Automata (UPTA) model, admitting an ecient priced zone implementation via Di erence Bound Matrices [Dil89] The model was used to consider traces for the time optimal scheduling of a steel plant and a number of job shop problems. The greater expressivity of LPTA also supports other measures of cost, like idle time, weighted idle time, mean completion time, earliness, number of tardy jobs, tardiness, ....

.... and frgZ the set of clock valuations obtained by delaying and resetting (w.r.t. r) clock valuations from Z respectively. That is, Z = fu d j u 2 Z; d 2 R 0 g and frgZ = fu[r 7 0] j u 2 Zg. It is well known using a canonical representation of zones as Di erence Bounded Matrices (DBMs) Dil89] that in both cases the resulting set is again e ectively representable as a zone. Using these operations together with the obvious fact, that zones are closed under conjunction, the post operations may now be e ectively realised using the zone based representation of symbolic states as ....

D. Dill. Timing Assumptions and Verication of Finite-State Concurrent Systems. In J. Sifakis, editor, Proc. of Automatic Verication Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 197-212. Springer{Verlag, 1989.

....techniques to prune parts of 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 ecient data structures (e.g. DBMs [7], CDDs [14] and DDDs [15] already used in the real time veri cation tools Uppaal and Kronos for reachability. The results of the present paper also extends the work in [2] which provides an algorithm for computing the accumulated delay in a timed automata. In this paper, we provide the basis for ....

David Dill. Timing Assumptions and Verication of Finite-State Concurrent Systems. In J. Sifakis, editor, Proc. of Automatic Verication Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 197-212. Springer{Verlag, 1989.

....version of regions, and is thus guaranteed to be extremely inecient and highly sensitive to the size of constants used in the models. As the rst contribution of this paper, we give for the subclass of UPTA an ecient zone representation of symbolic cost states based on Di erence Bound Matrices [Dil89] and give all the necessary symbolic operators needed to implement the algorithm. As the second contribution we show that, in analogy with Dijkstra s shortest path algorithm, if the algorithm is modi ed to always select from Waiting the (symbolic cost) state with the smallest minimum cost, the ....

....in Fig. 1 uses symbolic cost states, quite similar to how timed automata model checkers like Uppaal use symbolic states. Typically, symbolic states are pairs on the form (l; Z) where Z R C is a convex set of clock valuations, called a zone, representable by Di erence Bound Matrices (DBMs) Dil89] The operations needed for forward state space exploration can be eciently implemented using the DBM data structure. In the priced setting we must in addition represent the costs with which individual states are reached. For this we suggest the use of symbolic cost states, l; C) Table 1. ....

D. Dill. Timing Assumptions and Verication of Finite-State Concurrent Systems. In J. Sifakis, editor, Proc. of Automatic Verication Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 197-212. Springer{Verlag, 1989.

....of the LPTA model for scheduling problems was already illustrated in [BFH ] using the more restricted Uniformly Priced Timed Automata (UPTA) model. This model allows only a uniform cost rate for all locations, which admits an ecient priced zone implementation via Di erence Bound Matrices [Dil89] The model was used to consider traces for the time optimal scheduling of a steel plant and a number of job shop problems. The greater expressivity of LPTA also supports other measures of cost, like idle time, weighted idle time, mean completion time, earliness, number of tardy jobs, tardiness, ....

.... and frgZ the set of clock valuations obtained by delaying and resetting (w.r.t. r) clock valuations from Z respectively. That is, Z = fu d j u 2 Z; d 2 R 0 g and frgZ = fu[r 7 0] j u 2 Zg. It is well known using a canonical representation of zones as Di erence Bounded Matrices (DBMs) Dil89] that in both cases the resulting set is again e ectively representable as a zone. 5 Using these operations together with the obvious fact, that 3 In the example we assume that several automata A1 ; An can be composed in parallel with a CCS like parallel composition operator [Mil89] to ....

D. Dill. Timing Assumptions and Verication of Finite-State Concurrent Systems. In J. Sifakis, editor, Proc. of Automatic Verication Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 197-212. Springer{Verlag, 1989.

....version of regions, and is thus guaranteed to be extremely inecient and highly sensitive to the size of constants used in the models. As the rst contribution of this paper, we give for the subclass of UPTA an ecient zone representation of symbolic cost states based on Di erence Bound Matrices [Dil89] and give all the necessary symbolic operators needed to implement the algorithm. As the second contribution we show that, in analogy with Dijkstra s shortest path algorithm, if the algorithm is modi ed to always select from Waiting the (symbolic cost) state with the smallest minimum cost, the ....

....in Fig. 1 uses symbolic cost states, quite similar to how timed automata model checkers like Uppaal use symbolic states. Typically, symbolic states are pairs on the form (l; Z) where Z R C is a convex set of clock valuations, called a zone, representable by Di erence Bound Matrices (DBMs) Dil89] Table 1 shows common set operations on zones needed for the forward state space exploration algorithm of timed automata. In all cases the operations are eciently implementable using the DBM data structure. In the priced setting we must in addition represent the costs with which individual ....

D. Dill. Timing Assumptions and Verication of Finite-State Concurrent Systems. In J. Sifakis, editor, Proc. of Automatic Verication Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 197-212. Springer{Verlag, 1989.

....techniques to prune parts of 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 ecient data structures (e.g. DBMs [6], CDDs [12] and DDDs [13] already used in the real time veri cation tools Uppaal and Kronos for reachability. In this paper, we provide the basis for dealing with more general optimisation problems. In particular, we introduce the model of linear priced timed automata, as an extension of timed ....

David Dill. Timing Assumptions and Verication of Finite-State Concurrent Systems. In J. Sifakis, editor, Proc. of Automatic Verication Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 197-212. Springer{Verlag, 1989.

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D.Dill, \Timing Assumptions and Veri cation of Finite-State Concurrent Systems," Proc.CAV Methods for Finite State Systems, Grenoble, 1989.

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D.Dill, \Timing Assumptions and Veri cation of Finite-State Concurrent Systems," Proc.Workshop on Computer Aided Veri cation Methods for Finite State Systems, Grenoble, France, 1989.

No context found.

David Dill. Timing Assumptions and Veri cation of Finite-State Concurrent Systems. In J. Sifakis, editor, Proc. of Automatic Veri cation Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 197-212. Springer{Verlag, 1989.

No context found.

David Dill. Timing Assumptions and Veri cation of Finite-State Concurrent Systems. In J. Sifakis, editor, Proc. of Automatic Veri cation Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 197-212. Springer{Verlag, 1989.

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