on the formalization and comparison of coordination models and languages

On the Formalization and Comparison of Coordination Models and Languages

Gianluigi Zavattaro Department of Computer Science

University of Bologna

Validation02 - Genova - 22/11/2002

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Plan of the Talk Coordination Infrastructures Data- vs Event-driven coord.

(informally) Shared Dataspaces (formally) Publish/Subscribe (formally) Dataspace Pub/Sub Pub/Sub Dataspace + Global Op.


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Coordination Infrastructures: a Classification

A Data-driven Coordination Infrastructure TSpaces

An Event-driven Coordination Infrastructure Talarian SmartSockets


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Common Features No direct Communication

Communication mediated by the infrastructure

Space Uncoupled Communication No channel topology

Time Uncoupled Communication Asynchronous communication

Associative Communication Communication based on content or subject


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Motivation How much critical is the choice of the

kind of infrastructure in the design of a coordinated system?

Are event- and data-driven infrastructures interchangeable? Can each event-driven system be

reduced to an equivalent data-driven system without altering the internal behavior of the processes, and vice versa?


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The Units of Coordination Event-driven coordination

Processes raise events An event is delivered to the processes

which subscribed their interest to its specific type

Data-driven coordination Processes produce data A datum may be accessed (read or

consumed) from all process in the system


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Creation An event can be raised whatever is

the current state of the system A datum can be produced

whatever is the current content of the shared repository

The production of the Units of Coordination is Non-Blocking


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Lifetime An event plays a role in the system

until its multicast finishes Implicitly received/removed from the

system A datum remains in the shared

repository until it is explicitly withdrawn Explicitly read/consumed


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Visibility An event is visible only and

exactly to the subscribed processes Restricted visibility

A datum can be read/consumed by each process in the system Global visibility


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DS semanticsGraphically

rd(b).Qout(c).P

in(a).R

<b><a> <b

>eval(T).S

<c>

T


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PS semanticsGraphically

sub(e,P).Q

new(U).V

unsub(f,S).T

pub(e).R

on(e,P)on(e,Z)

on(f,S)

P

ZU


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Reducing DS into PS Mapping entities of Dataspaces

into entities in Pub/Sub Data = listeners Output = listener production Input = listener consumption Read = Input+Output


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The Reduction Function[[ 0 ]] = 0[[ K ]] = K (with K = [[ P ]])[[ out(a).P ]] = sub(ea,0).[[ P ]][[ in(a).P ]] = unsub(ea,0).[[ P ]][[ rd(a).P ]] = unsub(ea,0).sub(ea,0).[[ P

]][[ eval(P).Q ]] = new([[ P ]]).[[ Q ]]


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No Reduction of DS into PS A satisfactory reduction should preserve

at least termination [[ C ]] may terminate iff C may terminate

The existence of a terminating computation is Decidable in DS (reduction of DS to finite P/T

nets) Undecidable in PS (reduction of RAMs into

PS)Impossibility of any satisfactory

reduction


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Reducing PS into finite P/T nets

<a>

Q

Pin(a).Q

out(a).P


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Random Access Machine (RAM)

Registers: r1 … rn hold natural numbersProgram: sequence of numbered

instructions Inc(rj): add 1 to the content of rj and go to

the next instruction DecJump(rj,s): if the content of rj is not 0

then decrease by 1 and go to the next instruction; otherwise jump to instruction s


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Encoding RAM in PS(the idea)

DecJump(rj,s): Non-det. choice between

Decrement = loop until decrement succeeds

Jump = publish rj and jump to instruction s

on(in,[[insn]])

on(i1,[[ins1]])…

Instructionson(r1,pub(r1))…on(r1,pub(r1))

on(rm,pub(rm))…on(rm,pub(rm))

Registers


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Properties of the RAM encoding

Only termination is preserved: RAM iff [[ RAM ]] Oss: By C we mean the existence of a completed finite computation

Can we define also a divergence preserving encoding?Answer: no because the existence of an infinite computation is decidable


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Decidability of Divergence We express PS in terms of P/T nets

with transfer arcs (divergence is decidable [DFS98])

R

P

pub(e).Ron(e,P)

start(P,a)

sub(e,P).Q

Q


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Adding Global Operation We extend DS with a global

operation (inspired by copy-collect)

ccollect(a,P).Q

<a> <b>

<a><c>

P

P


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Reducing PS into DS Listeners = data

on(e,P) = lsteP

Subscribe = data production [[ sub(e,P) ]] = out(lsteP)

Unsubscribe = data consumption [[ unsub(e,P) ]] = in(lsteP)

Publish = count each kind of listeners [[ pub(e) ]] = ccollect(lsteP1,P1)…

ccollect(lstePn,Pn)


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Conclusion

DS calculus

PS calculus

TerminationUndecidable

TerminationDecidable

+ Glob. Operators

DivergenceDecidable

on the formalization and comparison of coordination models and languages

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