Integrated Modeling Using Finite State Machines and Dataflow Graphs - Signal Processing Systems - page 969

Fig. 10 Filter example dataflow graph: The ACFSMs ( Producer , Controller , Filter and
Consumer ) are connected via FIFO channels. The Filter actor has two inputs ( in and coeff )
from which tokens are consumed and one output ( out ) onto which tokens are produced

port A or on port B to forward to the output port O . If this decision should be
encoded in the actor instead, CAL provides a priority mechanism which creates a
non-reflexive, anti-symmetric, and transitive partial order relation on the transitions.
Actions which are lower in this partial order cannot be executed if there is at least
one action enabled which is higher in the partial order. To exemplify this, we can
look at the priority merge actor from Fig. 9 b which prioritizes the action FA before
action FB . Therefore, action FB can never be executed if there is a token present on
input port A .
With the priority extension, the formal model of a CAL actor consists of a triple
( σ 0 , τ , )

n

containing its initial actor state σ 0 ∈ Σ , its transition relation τ ⊆ Σ × S ×

m

S × Σ encoding actions and guards, and the partial order ⊂ τ × τ encoding the

priority relationship of the actions.

2.5 Extended Codesign Finite State Machines

The Extended Codesign Finite State Machine ( ECFSM ) Model of Computation
( MoC ) has been presented in [ 35 ] . As will be seen, the original Codesign Finite
State Machine ( CFSM ) MoC used in POLIS [ 2 ] is a special case of the ECFSM
MoC . Both models, however, are refinements of the Abstract Codesign Finite State
Machine ( ACFSM ) Model, also presented in [ 35 ] .
In this section, we will therefore first introduce the ACFSM Model of Compu-
tation, followed by the discussion of the refinement step which transforms a given
ACFSM into an ECFSM .An ACFSM is a formal model consisting of a network
of FSMs (in the following called actors) connected via unbounded FIFO channels .
As in CAL, tokens (also called events ) are transmitted across the channels carrying
data values of some data type. An example of such a dataflow network consisting of
several ACFSMs in Fig. 10 is shown.
Briefly, a single ACFSM consists of an FSM controlling the communication
behavior of the actor, transforming a finite sequence of input tokens into a finite
sequence of output tokens.
In order to formally describe the behavior of a single ACFSM , we will first look
at the behavior of the Filter actor from Fig. 10 . Its task is to filter a sequence
of pixels from the Producer actor by multiplying all pixels of a frame by a