DATAFLOW%20PROCESS%20NETWORKS

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DATAFLOW PROCESS NETWORKS

• Edward A. Lee
• Thomas M. Parks

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Abstract

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

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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

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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.

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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)

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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.

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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

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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

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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.

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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

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Firing Rules

• Definition
• R R1, R2, , RN
• Examples
• Select actor
• R1 , ?, T
• R2 ?, , F
• Nondeterminate merge
• R1 , ?
• R2 ?,
• These rules are not sequential.

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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.

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Relationship to Higher-order Function

• Define
• F map(f)
• where F(RX) 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.

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Sequential Process
Sequential ? continuous ? monotonic Sequential ? continuous ? monotonic
monotonic X ? Y ? F(X) ? F(Y)
continuous ?? X0, X1, s.t. X0 ? X1 ? , F(??) ?F(?)
sequential ?X X1, X2, ,Xp, ?i, 1?i?p, s.t. ?Y ? X where Yi Xi, F(Y) F(X), when F is continuous.

• Theorem if an actor function f has sequential
  firing rules, then the process F map(f) is
  sequential

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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

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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

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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

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Experimenting With Language Design

• Firing rules and strictness
• Recurrences and recursion
• Higher order function
• The tagged-token execution model
• Data types and polymorphism
• Parallelism