On the analysis of synchronous dataflow graphs: a system-theoretic perspective


ion of a model such that its analysis becomes cheaper, at the expense of a loss in accuracy, is common in various �elds where mathematical models serve to model real-world phenomena. In this chapter, we introduce such an abstraction for CSDF graphs: we show how a CSDF graph can be transformed into an HSDF graph that is either pessimistic (that is, conservative), or optimistic with respect to the CSDF graph. �is transformation comes at the expense of a loss in accuracy: the temporal constraints on the �rings of actors are, depending on the kind of approximation, relaxed or tightened with respect to the constraints imposed by the approximated graph. �e approximation involves the computation of linear bounds on the predecessor functions (see Chapter �) associated with actors and channels. We give approximations for both the actor �ring and the token transfer perspective, and compare their quality in terms of their estimation error. �e conservative approximations are temporal abstractions of the original graph: when feeding input to a system at a low enough rate, their temporal behaviour is indistinguishable from that of the approximated graph. At higher input rates, however, the system’s lower throughput becomes visible. Its performance is never better than that of the original graph. We highlight a particular application of such a temporal abstraction: any of its admissible schedules can be mapped to one that is admissible for the original graph. �is provides a computationally cheaper approach to computing admissible schedules for CSDF graph, at the expense of their not attaining maximum throughput. We start this chapter with a brief discussion on a class of discrete event systems that are relatively easy to analyse: those that are linear and shi�-invariant. �is sets a goal for the approximating transformations: they must yield linear and shi�invariant systems. �e transformation is described in Sections �.� and �.�. Section �.� discusses the quality of the approximations, and the chapter concludes with a discussion on related approaches in Section �.�. �.� L����� �����-��������� ������� Linearity and shi�-invariance are two most welcome properties of a discrete event system. A discrete event system is linear and shi�-invariant if it can be described by the following set of equations in max-plus algebra (see Chapter �): t(k + �) = A⊗ t(k)⊕ B ⊗ u(k), y(k) = C ⊗ t(k), (�.�) where A, B and C are matrices, u is the system’s input, t is the system’s state, and y the system’s output. Matrix A is the system’s state matrix. From this matrix, we

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@inproceedings{Groote2016OnTA, title={On the analysis of synchronous dataflow graphs: a system-theoretic perspective}, author={Elibertus de Groote}, year={2016} }