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DATAFLOW PROCESS NETWORKS

DATAFLOW PROCESS NETWORKS. Edward A. Lee Thomas M. Parks. Abstract. This paper presents a model of computation called “dataflow process networks”. Special case of Kahn process networks Relations with other dataflow models. Motivation.

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DATAFLOW PROCESS NETWORKS

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  1. DATAFLOW PROCESS NETWORKS Edward A. Lee Thomas M. Parks

  2. Abstract • This paper presents a model of computation called “dataflow process networks”. • Special case of Kahn process networks • Relations with other dataflow models

  3. Motivation • Programming methodology: “graphical dataflow programming” • Visual syntax • Hierarchy • Examples: Khoros, Ptolemy, SPW, COSSAP, and the DSP Station. • Most environments do not define a language in any strict sense • Can be either interpreted or compiled

  4. One-way FIFO process process Process Networks • A process is a mapping from one or more input sequences to one or more output sequences • A process network: concurrent processes communicate only through one-way FIFO channels with unbounded capacity.

  5. Kahn Process • The process is constrained to be continuous • Prefix ordering of sequences: X  Y • Set of sequence can be ordered as well: X  Y, if Xi Yi for each i • Increasing chain of sequences:  = {X0, X1, …}, where X0  X1  …. • Least upper bound of  :  • Functional process F: SpSq • Continuity F() = F() • Monotonicity X  X’  F(X)  F(X’)

  6. Network of Processes • A network: a set of relations between sequences. X = F(X,I) • Any X that forms a solution is called a fixed point. Continuity of F implies that there will be exactly one “minimal” fixed point. • Execute the network by first setting I =  and finding the minimal fixed point, then by iterative computation to find other solutions.

  7. Nondeterminism • A useful property is an ability to express nondeterminism. • Nondeterminism leads to failure of continuity • It can be added to Kahn networks by any of the five methods: • Allowing processes to test inputs for emptiness • Allowing processes to be internally nondeterminate • Allowing more than one processes to write to a channel • Allowing more than one processes to consume data from a channel • Allowing processes to share variables • Example

  8. B A D E C Example of Nondeterminism • Merge node D • May be nondeterminate, may also be determinate • If D is a nondeterminate merge, then it is not a Kahn process network

  9. Streams • One camp defines streams recursively, using cons-like list constructors and usually treats them functionally using lazy semantics. Another camp sees streams as channels. There is no concept of simultaneity of tokens in the channel model. • A unique approach blends the benefits of a declarative style with the simplicity of the channel model • A more general approach is to associate with each stream a “clock”, which defines the alignment of tokens in different streams. • A useful stream model must be as good at losing data as it is at storing data.

  10. Dataflow Process Networks • Dataflow actor • When it fires, it maps input tokens into output tokens • Firing • Consumes input tokens and produces output tokens • A sequence of such firings is a particular type of Kahn process that we call a dataflow process; • a network of such processes is called a dataflow process network. • Firing rules • Specify when an actor can fire

  11. T select F Control DATA INPUT merge DATA OUTPUT Firing Rules • Definition: R = {R1, R2, …, RN} • Examples: • Select actor: • R1 = {[*], , [T]} • R2 = {, [*], [F]} • Nondeterminate merge • R1 = {[*], } • R2 = {, [*]} • These rules are not sequential.

  12. Sequential Firing Rules • Identifying sequential firing rules • For the example of select: • j = 3. • Subsets: {R1} and {R2} • R1 = {[*], , } and R2 = {, [*], } • Repeat till all modified firing rules become empty • For the nondeterminate example of the merge node, the procedure fails at step 1.

  13. Relationship to Higher-order Function • Define F = map(f) where F(R:X) = f(R):F(X) • The definition is recursive • Typically f requires only some finite number of tokens on each input, while the function returned by F can take infinite stream argument.

  14. Sequential Process • Theorem: if an actor function f has sequential firing rules, then the process F = map(f) is sequential

  15. …|x3|x2|x1 A B Relationship to Kahn Process Networks • A special case of Kahn process networks • Suppose A produces 1 token each process while B consumes 3 each process • Blocking read for B  scheduling of A and B

  16. Execution Models • A variety of execution models associated with a dataflow process network. • Concurrent processes • Dynamic scheduling • Static scheduling • Compilation of dataflow graphs • Tagged token model

  17. Experimenting With Language Design • The Ptolemy system • Synchronous dataflow domain (SDF) • Dynamic dataflow domain (DDF) • Boolean dataflow domain (BDF) • Visual hierarchy • Firing subgraphs – the balance equations • Side effects and state • Function arguments • Parameters and input streams

  18. Experimenting With Language Design • Firing rules and strictness • Recurrences and recursion • Higher order function • The tagged-token execution model • Data types and polymorphism • Parallelism

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