J. Bengtsson, B. Jonsson, J. Lilius, and Wang Yi. Partial order reductions for timed systems. In Proceedings of CONCUR'98, volume 1466 of LNCS, pages 485--500, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....between them. The formula of a global step is the conjunction of step formulae constructed for all automata. Private time scale composition The behaviors of loosely coupled automata that make independent transitions often can be encoded by formulae with less variables. The idea, inspired by [BJLY98] is based on expressing the steps of each automaton using a private time scale and on the synchronization of those time scales whenever required, i.e. only when automata interact. Each automaton i uses its own time stamp variables T i such that its corresponding date variables are # i = T ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed systems. In Proceedings of Concur'98, volume 1466 of LNCS, pages 485--500. Springer, 1998.

....it is possible to reduce branching in the timed state space by adding fewer relations to the set. Local time semantics and partially ordered sets (POSETs) remove orderings in the zone on sets of independent concurrent signal transitions reducing the representation size of the timed state space [20, 21, 22, 23, 24, 25]. POSET reduction in the timing analysis of Timed Petri nets (TPN) Petri nets with timers on the places yields a significant reduction in the number of zones associated with each marking [24] The algorithm in [24] implements the POSET reduction on concurrent independent signal transitions. ....

....Timed event level structures (TELs) are a more natural model for circuits [25] Extending BAP to support TELs or other circuit models will make it directly applicable to many circuits. Partial order reduction has been successfully applied to further improve timed state space exploration [28, 29, 20, 21]. This technique considers a restricted ordering of concurrent independent transitions in a circuit. The work presented here can be extended to support partial order reduction. Other work of interest includes: adding in correlation to model on chip delay variations; introducing an inertial delay ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed systems. In Proc. International Conf. on Concurrency Theory, pages 485--500, 1998.

....in the system. In this example, either clock C is reset to 0, or the output X is inverted to match its function F . A system is the parallel composition of several timed automaton. A timed automaton is a suitable model for verification as shown in [19, 20, 21, 22, 23] Work by Bengtsson et al. in [24] and Minea in [25] develop partial order techniques to reduce the cost of verification in timed automata. Work by Bozga uses symbolic methods to help contain the verification cost [20, 26, 27, 28] It is important to note that timed automata support both time and Boolean functions. They are very ....

....it is possible to reduce branching in the timed state space by adding fewer relations to the set. Local time semantics and partially ordered sets (POSETs) remove orderings in the zone on sets of independent concurrent signal transitions reducing the representation size of the timed state space [10, 24, 25, 57, 65, 66]. POSET reduction in the timing analysis of Timed Petri nets (TPN) Petri nets with timers on the places yields a significant reduction in the number of zones associated with each marking [66] The algorithm in [66] implements the POSET reduction on concurrent independent signal transitions. ....

[Article contains additional citation context not shown here]

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi, "Partial order reductions for timed systems," in International Conference on Concurrency Theory, pp. 485-- 500, 1998. 210

....and TCTL [ACD93] The practical applicability of model checking is strongly restricted by the state explosion problem. Therefore, many di erent reduction techniques have been introduced in order to alleviate the state explosion. The major methods include application of partial order reductions [BJLY98,DGKK98,Lil99,Pag96,Pel96,PP01,WG93,YS97] symmetry reductions [ES95] abstraction techniques [DGG94,DT98] BDD based symbolic storage methods [Bry86,McM93] and SAT related algorithms [BCC 99,CBRZ01,HN01,PW01,PWZ02b] Bounded model checking (BMC) based on SAT methods has been recently ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed systems. In Proc. of CONCUR'98, volume 1466 of LNCS, pages 485-500. Springer-Verlag, 1998.

....work has utilized a timed automaton to provide a low level model for a circuit. It is a state based specification language where transitions between states are governed not only by Boolean functions defined over inputs, but clock valuations too. Its expressiveness lends itself to verification [1,6,11,7,16,4,19]. The expressiveness, however, is not always required for synthesis; thus, it needlessly complicates the analysis problem. A Petri net based representation is an alternative circuit model to a timed automaton. It is a transition based specification language where transitions are governed by time ....

....simplifies specification. LPNs are a refinement of TEL structures described in [2,3] LPNs restrict conflict to the Petri net formalism and facilitate a partial order reduction on the reachable state space. Partial order reduction is an important tool in mitigating state explosion in verification [9,28,15,17,4,19]. Partial order reduction is applied to synthesis in [25,31] The approach in [25] is an unfolding technique that is applied to untimed specifications. Not only is it not clear if the technique can be e#ciently applied to a timed model, the technique ignores hierarchy in the specification; thus, ....

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Bengtsson, J., B. Jonsson, J. Lilius, and W. Yi, Partial order reductions for timed systems, Proc. International Conf. on Concurrency Theory (1998), 485--500.

....the inequalities in # # are outside the scope of DL. After eliminating t we obtain #=i (C # i C i ) C # j C j ) with numerical constraints that relate 4 numerical variables. This can be, however, circumvented by a change of variables which has an intuitive meaning (see also [BJLY98] Consider a state extended with a time stamp T . For every clock C i , the variable X i = i represents the last time when C i was reset (we use the notation = T for the whole transformation) It is not hard to see that an (X , T ) valuation gives a state representation isomorphic to ....

....values correspond to the same time instant. When the automata are loosely coupled it might be more economical to express the steps of each automaton using its private time scale and impose synchronization between those time scales only when the automata interact (this approach was introduced in [BJLY98] as an attempt to apply partial order methods to timed automata) For each i we use a different time stamp variable T i (T = T i ) such that the values of its date variables are i = T i i . Then we have, for every i and a reset # i , T i ) Cm## i X # m = T i X # m = ....

J. Bengtsson, B. Jonsson, J. Lilius and W. Yi, Partial Order Reductions for Timed Systems, Proc. Concur'98, 485-500, LNCS 1466, Springer, 1998.

.... symbolic state space exploration: an integration of partial order reduction techniques and symbolic state space exploration [2] # partial order reductions for timed systems: the problem of clock synchronizations causing partial order reductions to be less efficient in timed systems is overcome [6], and # reducing the number of clock variables: active clocks are first detected and then clocks that are always equal are reduced into one [10] Besides the above implementable manipulators, we have developed our own manipulators, namely read write reduction, clock shielding,andtimed ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed systems. In to appear in Procs. CONCUR '98, 1998.

....of timed automata that is needed. Results to justify the various definitions are also presented. There are two pieces of related work. 7] introduces a partial order model for timed systems. However it is based on the existence of an independence relation on the transition relation. [3] also introduces a partial order model. But the definition is based on a product of processes construction. There is no discussion of implementation in both these cases. In the next section we present a quick review of distributed automata and timed automata. The rest of the paper is concerned ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial Order Reductions for Timed Systems. In D. Sangiorgi and R. de Simone, editors, CONCUR 98, volume LNCS-1466, pages 485--500. Springer Verlag, 1998.

....automata world from the successful development in the timed automata world. Moreover, the fact that the translation is compositional does not only simplify the translation task, but also let us profit from partial order and compositional techniques already developed for timed automata (see e.g. [32, 10, 31, 12]) Related Work The aim of our work is to allow the possibility of verification on a stochastic model by translating it into a non stochastic model. In this way we loose the measure of the property that we want to verify and can only assert whether it is possible the property holds with ....

....the resulting network of timed automata could be a direct input to techniques and tools that partially or totally consider the compositional characteristic of a system. For instance, recently new results on partial order techniques for the verification of timed automata have been introduced (e.g. [32, 10, 31]) Another recent approach to compositional analysis of timed automata ensures liveness by construction [12] more precisely, by doing some structural checking of the component timed automata one can conclude that the composed automaton is timelock and deadlock free. 7FinalRemarks We defined a ....

[Article contains additional citation context not shown here]

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed systems. In D. Sangiorgi and R. de Simone, editors, Proceedings CONCUR 98, Nice, France, volume 1466 of Lecture Notes in Computer Science, pages 485--500. Springer-Verlag, 1998.

....To deal with this (unavoidable) problem we introduce a method, allowing the user to guide the model checking according to certain chosen strategies. Each strategy will contribute with a reduction of the search space, but in contrast to fully automatic reduction methods like partial order reduction [33] it is up to the user to guarantee preservation of schedulability. However, if a schedule is identified via the guided search, the schedule is indeed a valid one for the original model. Since we are not interested in optimal schedules this is su#cient. To be able to run the generated control ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial Order Reductions for Timed Systems. In Proc. of CONCUR '98: Concurrency Theory, volume 1466 of Lecture Notes in Computer Science, pages 485--500, 1998.

.... 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 [BJLW98,Min99] Our approach is closely related to [DGKK98] from which we draw the idea of the covering relation, and to [GKPP99,PSGK00] from which we take the general method of partial order reductions preserving branching time properties. The partial order approach presented in [VP99] works for Time ....

J. Bengtsson, B. Jonsson, J. Lilius, and Y. Wang, Partial Order Reductions for Timed Systems, LNCS 1466 (1998), 485-500.

....ones obtained from the hierarchical structure specified by a system designer. Finally, our cluster based algorithm is compatible with the upgrade of SPIN s engine for timed systems from [4] It is very likely that it can be combined with techniques for partial order reduction for timed automata [3, 5, 17]. ....

J. Bengtsson, B. Jonsson, B. Lilius, and W. Yi. Partial Order Reductions for Timed Systems. In D. Sangiorgi and R. de Simone, eds, Concurrency Theory, CONCUR '98, LNCS 1466, p. 485--501. Springer, 1998.

....process for finding the reachable state space under timing is called timing analysis ; and it is paramount to producing more e#cient circuits. State explosion is a major impediment to timing analysis. Partial order reduction addresses this issue by exploring a portion of the reachable state space [5, 6, 7, 8]. However, as the goal of analysis in this work is synthesis, a full exploration is required. An # This research is supported by SRC contract 97 DJ 487. other approach is to implicitly store the state space in a directed acyclic graph that is an unfolding of the system. Circuit synthesis is ....

....is a partially ordered set relating various clock values or transition times, it is possible to reduce branching in the time state space by adding fewer relations to the set. Local time semantics or partially ordered sets (POSETs) remove orderings in the zone on sets of independent transitions [7, 8, 21, 22] reducing the representation size of the timed state space. POSET reduction in the timing analysis of Timed Petri nets (TPN) Petri nets with timers on the places yields a significant reduction in the number of zones stored at each state [23] The algorithm implements the POSET reduction on ....

[Article contains additional citation context not shown here]

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed systems. In Proc. International Conf. on Concurrency Theory, pages 485--500, 1998.

....systems the technique of partial order reduction has in several practical cases proved extremely useful in dealing with the phenomena of state explosion. The technique exploits independence between components in order to settle model checking problems by only examining part of the state space. In [BJLY98] a serious attempt of providing a partialorder reduction method for timed systems based on a local time semantics for networks of timed automata is given. However, the implicit global synchronization on time progress for timed systems has proved to be a major obstacle in obtaining reductions and ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial Order Reductions for Timed Systems . In Partial Order Reductions for Timed Systems, Nice, France. Springer Verlag, 1998.

.... 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 defined only for linear time properties either for Time Petri Nets [YS97, Lil98] or for Timed Automata of standard [Pag96, DGKR98] or local semantics [BJLW98, Min99]. Our approach is closely related to [DGKR98] from which we draw the idea of the covering relation, and to [GKPP99, PSGK00] from which we take the general method of partial order reductions preserving branching time properties. 3 Time Petri Nets Let Q denote the set of non negative ....

J. Bengston, B. Jonsson, J. Lilius, and Y. Wang, Partial order reductions for timed systems, LNCS, vol. 1466, Springer-Verlag, 1998, pp. 485--500.

....each untimed state has at least one geometric region associated with it for every firing sequence that can result in that state. In highly concurrent systems where many interleavings are possible, the number of geometric regions per untimed state can be huge. Some researchers [10] 11] 12] [13] have attacked this problem by reducing the number of interleavings explored using the partial order techniques developed for untimed systems. These algorithms reduce verification time by exploring only part of the timed state space, but the improvement is dependent on the property to be verified. ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed systems. In International Conference on Concurrency Theory, September 1998.

....histories are known as streams, and may be discrete sequences or continuous. The behaviours of processes are combined using parallel composition with feedback, and re nement is de ned in terms of simulations between abstract and concrete systems. Partial order reduction techniques have been used [5] to remove implicit clock synchronisation between processes in a network of timed automata. While this avoids reasoning about interleavings of independent transitions in di erent processes, it requires the resynchronisation of time variables when processes communicate. Acknowledgements I wish to ....

J. Bengtsson, B. Jonsson, J. Lilius and W. Yi, Partial Order Reductions for Timed Systems, in D. Sangiorgi and R. de Simone (Eds.) Concurrency Theory (CONCUR'98). Lecture Notes in Computer Science 1466, Springer-Verlag, 1998.

....practical tools. We are working on techniques to obtain a reduced automaton with the same duration problem. As future work, we would like to adapt some recently presented optimization techniques to our framework (e.g. 10; 20; 4] In particular, we believe that partial order techniques (see [4]) can be adapted to check LDI which depends on the locations of just one automaton of a parallel composition. 18 Delta F .Pieniazek, V. Braberman Another interesting topic of research is the study of on the fly techniques to avoid the construction of the whole reachability graph (unfolding the ....

J Bengtsson, B Jonsson, J Lilius, and Wang Yi. Partial order reductions for timed systems. In Proceedings of CONCUR '98, September 1998.

.... after time ffi from state s = m; c) giving a new state, s 0 = m 0 ; c 0 ) as follows: m 0 = m n ffl t [ t ffl ; 5) c 0 (t) ffi 0 if t 2 enabled(m 0 ) enabled(m) c(t) ffi else : 6) This is denoted by s 0 = fire(s; t; ffi) 4 p5 t2 p6 [1,3] 1,4] 0,3] [2,2] p1 t1 p2 p4 p3 t3 t4 (a) The net N 1 t2 [1,3] 1,4] p1 t1 p2 p4 p3 t3 [0,3] p5 (b) The net N 2 Fig. 2. Two example time Petri nets The behavior of a time Petri net is described in terms of a ring schedule. Denition 2.5 A ring schedule of a time Petri net is a nite or innite ....

....for determining whether a marking m is reachable in the time Petri net N. Proof. Along the lines of the proofs in e.g. 8] 2 4 Conclusions The use of persistent sets is a standard technique in the context of untimed systems (cf. 8] while for timed systems only a few proposals exists: [2] for timed automata, and [14] for time Petri nets. In this work we have proposed a new semantics for time Petri nets that does not store the ring order into the timing constraints. This allows us to lift the notion of independence from untimed Petri nets, and it becomes possible to directly apply ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed system. In Proceedings of CONCUR'98, 1998, to appear.

....the reachable states From the above discussion it is clear that since we consider time to be a continuous quantity the set of states of a time Petri net is in nite. In this section we will show that this in nite state space can be partitioned into equivalence 4 p5 t2 p6 [1,3] 1,4] 0,3] [2,2] p1 t1 p2 p4 p3 t3 t4 (a) The net N 1 t2 [1,3] 1,4] p1 t1 p2 p4 p3 t3 [0,3] p5 (b) The net N 2 Figure 2: Two example time Petri nets classes that will consist of markings and sets of inequations that constrain the possible occurrence times of the enabled transitions. The idea of ....

....for determining whether a marking m is reachable in the time Petri net N. Proof: Along the lines of the proofs in e.g. 8] 3. 9 20 4 Conclusions The use of persistent sets is a standard technique in the context of untimed systems (cf. 8] while for timed systems only a few proposals exists: [2] for timed automata, and [14] for time Petri nets. In this work we have proposed a new semantics for time Petri nets that does not store the ring order into the timing constraints. This allows us to lift the notion of independence from untimed Petri nets, and it becomes possible to directly ....

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed system. In Proceedings of CONCUR'98, 1998, to appear.

No context found.

J. Bengtsson, B. Jonsson, J. Lilius, and Wang Yi. Partial order reductions for timed systems. In Proceedings of CONCUR'98, volume 1466 of LNCS, pages 485--500, 1998.

No context found.

J. Bengtsson, B. Jonsson, B. Lilius, and W. Yi. Partial Order Reductions for Timed Systems. In D. Sangiorgi and R. de Simone, eds, Concurrency Theory, CONCUR '98, LNCS 1466, p. 485--501. Springer, 1998.

No context found.

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial Order Reductions for Timed Systems. In CONCUR'98. LNCS 1466, 1998.

No context found.

J. Bengtsson, B. Jonsson, J. Lilius, and W. Yi. Partial order reductions for timed systems. In Proc. of CONCUR'98, volume 1466 of LNCS, p. 485-500. SpringerVerlag, 1998.

No context found.

Bengtsson, J., Jonsson, B, Lilius, J., Yi, W., Partial Order Reductions for Timed Systems, CONCUR'98, LNCS 1466, pp. 485-501, 1998.

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