DATAFLOW PROCESS NETWORKS

Presentation Transcript

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

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

One-way FIFO

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.

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’)

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.

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

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

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.

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

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.

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.

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.