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...paces generated in isolation are much larger than the local states actually reached), or to use a version of Saturation that does not require a Kronecker encoding for N , such as the one described in =-=[28]-=-. Finally, since the same model decomposition and variable ordering is used for Saturation and breadth–first iteration, the algorithms generate isomorphic “final” MDDs for S. Several important conclus...

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...systems. The algorithm was first defined for transition relations that admit a Kronecker encoding. While this encoding always exists, it might be unwieldy, thus the approach was not always practical. =-=[11]-=- avoids the Kronecker encoding by conjunctively partitioning the transition relation of each event into groups, encoded by matrix diagrams with an identity reduction. [5] allows an even finer partitio...

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...malisms to defineitsownformat.Examplesofvalidtranspositionshavebeen investigatedin the context of PEPA [13], [12] and SGSPN [9]. We are aware of other sophisticated model representations, such as MxD =-=[14]-=-, which are not entirely dependent on a Kronecker description. However, the focus of this work is to enhance the numerical solution of Kronecker-based models. SAN formalism allows complexinteractionsa...

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...the Kronecker-based schemes [CM99,CMS03] and for the symbolic synchronization approaches [Sie98,Sie02,KS02,Par02]. In order to extend the saturation technique of [CMS03] to a general class of models, =-=[Min04]-=- describes an event-oriented approach, where a kind of dependency relation among events, as well as an Apply-algorithm for building the cross-product of two matrix diagrams, is employed. This allows [...

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...1 0 0 1 2 0 1 2 Figure 2.6 MTMDD on the left shows the quasi-reduced form of the MTMDD in Figure 2.5 and the one on the right shows its fully-reduced form. 2.2.4 Matrix Diagrams Matrix Diagrams(MxDs) =-=[18, 24]-=- are used to encode functions of the form (X × X ) → {0, 1}(X is described in Section 2.2.3). In modelling a sytem, the variables used to represent the current state are called unprimed variables or f...

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...ed many insights in dealing with compact and efficient descriptions of reachable state spaces (RSS) for SPN models. Basically, Buchholz and Kemper [10], Ciardo, Lüttgen and Siminiceanu [11] and Miner =-=[12]-=- have proposed efficient ways to deal with large reachable state spaces found in SPN models within huge product state spaces. Similar solutions for SAN formalism [5] do not exist for generic models an...

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...ion algorithm was first defined for transition relations that admit a Kronecker encoding. While this encoding always exists, it might be unwieldy, thus the approach was not fully general in practice. =-=[19]-=- avoids the Kronecker encoding by partitioning the transition relation of each event into groups, encoded by matrix diagrams [17], while [13] allows an even finer partition for the transition relation...

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...ymbolic hybrid model checker will be developed. This tool will utilize several well–established techniques for model checking with MDDs, and some recent advancements in state space generation (e.g., =-=[11, 34]-=-). However, for a hybrid model, it is anticipated that additional information will be necessary for states or for edges in the finite state machine, in particular constraints that arise during counter...