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Integrated Modeling Using Finite State Machines and Dataflow Graphs

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Handbook of Signal Processing Systems

Abstract

In this chapter, different application modeling approaches based on the integration of finite state machines with dataflow models are reviewed. Many well-known Models of Computation (MoC) that are used in design methodologies to generate optimized hardware/software implementations from a model-based specification turn out to be special cases thereof. A particular focus is put on the analyzability of these models with respect to schedulability and the generation of efficient schedule implementations. Here, newest results on clustering methods for model refinement and schedule optimization by means of quasi-static scheduling are presented.

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Notes

  1. 1.

    The ‘*’-operator is used to denote Kleene closure of a value set. It generates the set of all possible finite sequences of values from a value set, that is \({X}^* = \cup {n \in {\mathbb {N}_0}}:X^n\). As is customary, \(\mathbb {N}_0 = \{0,1,2,3,\ldots \}\) denotes the set of non-negative integers.

  2. 2.

    In some dataflow models that abstract from token values, the delay function may only return a non-negative integer that denotes the number of initial tokens on the channel. In such a context, the number of initial tokens may also be called the delay of a channel.

  3. 3.

    As is customary, \(\mathbb {N} = \{1,2,3,\ldots \}\) denotes the set of positive integers.

  4. 4.

    Note that in contrast to previous editions of this handbook, the separation of functionality into actions and guards has been explicitly introduced in the definition.

  5. 5.

    We use the ‘.’-operator, e.g., a.I, for member access of tuples whose members have been explicitly named in their definition, e.g., member I of actor a ∈ A from Definition 5. Moreover, this member access operator has a trivial extension to sets of tuples, e.g., \(A.I = \bigcup { }_{a \in A} a.I\), which is also used throughout this document.

  6. 6.

    Notice that the enabling rate \(\operatorname {\mathbf {req}}\) as well as the input consumption rate and the output production rate functions \(\operatorname {\mathbf {cons}}\) and \(\operatorname {\mathbf {prod}}\) are no longer explicitly given but can be derived from the transition guard and the action, respectively.

  7. 7.

    The definition of a cluster FSM (Definition 9) has been extended compared to previous editions to allow for the representation of more general schedules within the cluster FSM.

  8. 8.

    The initial state q 0 might be an exception to this observation as the cluster might have an initial state where tokens can be produced without consuming additional inputs. In contrast to previous editions of this handbook and to ease the visualization, these cluster states are represented by the number of firings of each actor in the cluster instead of the number of tokens consumed and produced on each of cluster input and output ports. Both representations are equivalent and can be transformed into each other.

  9. 9.

    In the following, we will drop the ‘\(g_{\gamma _{}}.\)’-prefix from various notations when the cluster is clear from context, e.g., I instead of \(g_{\gamma _{}}.I\).

  10. 10.

    In reality, the cluster will not undo any actor firing and this should be thought of as delayed production of tokens by a dynamically scheduled cluster in contrast to a composite actor implementing a QSS. A QSS is required to always produce the maximal number of output tokens from a minimal number of input tokens and, hence, will never delay the production of tokens on its output ports.

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Authors and Affiliations

  1. University of Erlangen-Nuremberg, Hardware-Software-Co-Design, Erlangen, Germany

    Joachim Falk & Jürgen Teich

  2. University of Rostock, Applied Microelectronics and Computer Engineering, Rostock-Warnemünde, Germany

    Kai Neubauer & Christian Haubelt

  3. Valeo Siemens eAutomotive Germany GmbH, Erlangen, Germany

    Christian Zebelein

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  1. Joachim Falk
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  2. Kai Neubauer
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  3. Christian Haubelt
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  5. Jürgen Teich
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Correspondence to Christian Haubelt .

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Editors and Affiliations

  1. Department of ECE and UMIACS, University of Maryland, College Park, MD, USA

    Shuvra S. Bhattacharyya

  2. Leiden Embedded Research Center, Leiden University Leiden Institute Advanced Computer Science, Leiden, The Netherlands

    Ed F. Deprettere

  3. RWTH Aachen University Software for Systems on Silicon, Aachen, Germany

    Rainer Leupers

  4. Department of Pervasive Computing, Tampere University of Technology, Tampere, Finland

    Jarmo Takala

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Falk, J., Neubauer, K., Haubelt, C., Zebelein, C., Teich, J. (2019). Integrated Modeling Using Finite State Machines and Dataflow Graphs. In: Bhattacharyya, S., Deprettere, E., Leupers, R., Takala, J. (eds) Handbook of Signal Processing Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-91734-4_23

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