A Pragmatic View of Model of Computation

1
A Pragmatic View of Model of Computation

• Xinping Zhu, Wei Qin
• Princeton University
• 11/1/2000

2
What is a model of computation?

• What is computation?
• Java Applet running on a web browser
• Baseball Game
• state players on base, score, count
• action pitch, swing
• Protein Synthesis
• input DNA
• output protein transcribed from gene in
  DNA
• Human Perception
• input 3D object
• output internal representation of object

3
What is a model of computation? (continued)

• What is computation formal way ?
• A computation is a specification for
  transformation of one instance set of data
  structures or objects to some other instance set
  of data structures or objects.
• A computation is a process which leads to
  satisfaction of a set of constraint specification
  .
• A computation is an ordered sequence of execution
  of a (possibly dynamic) set of primitive units of
  computation.
• Computation is a recursive and hierarchical
  concept. A computation may be primitive in one
  view and composed in another view.

4
What is a model of computation?(continued)

• What is model of computation (MOC)?
• A formal, abstract definition of a computer.
• Law of physics of concurrent components
• Ontology what they are
• Protocols how they communicate
• Epistemology what information they share
• A formal representation of concurrency Edward.
  Lee
• E.g.
• DE,CT,CSP,PN,DDE,S/R,SDF,FSM,PS
• References
• Edward A. Lee, Embedded Software An Agenda
  for Research, UCB ERL Memorandum M99/63.

5
The Actor Model of Computation

• An actor is a reactive entity. In response to a
  message,
• an actor can
• Create a new actor,
• Send a message to an acquaintance actor, or
• Change its internal behaviour.
• Actors have unique mail addresses.
• Messages (potential method invocations) are
  buffered in a mailbox.
• Actors communicate only via asynchronous message
  passing.
• In the actor model, there is guaranteed message
  delivery.

Ref. Gul A. Agha. Concurrent Object-Oriented
Programming''. Communications of the ACM,
33(9)125-141, Sep 1990.
6
Actor
The actor model or paradigm was created by Carl
Hewitt of MIT in the early 1970s, but the
work on the Actor concurrency model is largely
due to Agha.
Extension of the concept of objects to concurrent
computation.
Problem Hierarchy
7
MOC in Parallel Computation

• Parallel Random Access Machine (PRAM)
• If there is one model of parallel computation
  which stands out from the rest as being
  reasonably widely accepted, it is PRAM.
• It merely consists of a number of processes
  sharing a global random access memory, reading
  data from it, writing data to it and performing
  local computations. All processors perform one of
  these operations at a time in lock-step
  synchrony.
• Difficulty
• Inherently unrealistic model Synchronize every
  step
• Performance penalty
• Alternative Hierarchical PRAM, Bulk-Synchronous
  Parallel(BSP)

8
More Models of Computation

• Domain of Embedded Software
• Using special domain specific knowledge. E.g. air
  flight control,DSP
• Considering time in a model of computation is
  always cumbersome which tends to be ignored.
• Real-time system put a more serious challenge on
  current software development.
• More efforts are put on the exploitation of
  inherent parallelism both in computer
  architecture and software which means more
  understanding of the model of concurrency.

9
Continuous Time (CT)

• Components communicate via time continuous
  functions. Used for analog circuitry,
  interactions with sensors and actuators and other
  physical systems

10
Synchronous/Reactive Models (S/R)

• Global clock defines discrete points at which
  signals may have values
• Components respond to inputs
• Esterel an example implementation
• Example specification Emit output Received both
  as soon as signals A and B have occurred. Reset
  when there is a reset signal.
• example from ftp//ftp.esterel.org/esterel/pub/pap
  ers/primer.pdf

11
Discrete Event Models

• Events communicate the value of a variable with a
  time stamp
• No global clock, but globally consistent concept
  of time
• Distributed DE model
• Events communicate the value of a variable with a
  connection-specific time stamp
• The local time of an actor is the minimum of the
  time on input connections

x 0 at t 0 x 1 at t 5 x y/x at t 12
y 0 at t 0 y 1 z at t 4 y x z at t
9 y x z at t 15
z 0 at t 0 z 1 at t 3 z 8 - x at t
14
12
MoC Cycle Driven Models

• A simplified case of DE
• Each component has a clock
• Computations occur in a component at each clock
  cycle (i.e. like discrete events, but
  computations occur at regular intervals)

13
Synchronous Message Passing

• Components are processes (a process is a series
  of operations)
• Processes communicate with instantaneous
  transactions
• When two processes communicate, the first to be
  ready will stall until the other is ready
• E.g. resource sharing of hardware functional
  units, such as a multiplier

14
Asynchronous Message Passing

• Components are processes
• Processes communicate via channels that can
  buffer the messages
• Sender doesnt have to wait for receiver to be
  ready
• MoC Process Networks(PN) asynchronous message
  passing where input sequences are mapped into
  outputs by processes
• Dataflow models processes constructed out of
  process networks
• Adding time in PN using timestamp in messages

15
Questions

• Where is our stand in Model of Computation?
• Is it always better to think more formally than
  more Ad-hoc?
• Do we need a new model of computation?
• Where is the pragmatic point of view in model of
  computation?