Desynchronization and distributed deployment of

synchronous systems

Albert Benveniste – Inria

2002

The problem

• Ensure a smooth migration throughout the different phases of embedded systems design

• As analysis reveals, the diversity of communication/concurrency paradigms, throughout the design process, is a serious difficulty

SystemFrom

Components

System on Chip

Control engineeringMatlab/Simulink…Domain specific

Functional aspects

Model engineeringUML

System architecture

Performance, timelinessFault-tolerance

Non-functional aspects

Deployment architectureMiddleware

Bus, protocolsTasks

Device

start()stop()

Operator<<Actor>>

0..*1 0..*1

controls

: Operator

: Device

start( )

stop( )

ControllingSite RemoteSite

TCP/IP

: Operator

: Device

Class diagram Sequence diagram

Statecharts

Idle

Active

start stop

Implementation diagram

SystemFrom

Components

Model engineeringUML

System architecture

Performance, timelinessFault-tolerance

Non-functional aspects

Control engineeringMatlab/Simulink…Domain specific

Functional aspects

System on Chip

Deployment architectureMiddleware

Bus, protocolsTasks

MultiformMultiformModel ofModel of

communicationcommunication

Model engineeringComponents

looseloose

timelinessNon-functional aspects

timedtimed

Functional modelsEquations + states

synchronoussynchronous

Code generationGlobally AsynchronousGlobally AsynchronousLocally SynchronousLocally Synchronous

TasksSchedulingScheduling

Time-triggeredTime-triggered

Zooming on

Synchrony&

Asynchrony

Synchrony

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] |||

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

Synchrony

loop % unique non terminating while loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] |||

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

Synchrony

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] ||| % perfectly synchronous parallel composition

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

Synchrony

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] |||

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

Synchrony

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] |||

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

?X 3 -2 5 0 -1 -3 2 1

?Y 2 1 5 3

!Z * 3 6 8

Synchrony

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] |||

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

Synchrony

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] |||

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

?X 3 -2 5 0 -1 -3 2 1

?Z * 3 6 8

!V -4 0 -2 -6

Synchrony

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] ||| % synchronizes the two blocks by unification

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

Synchrony

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] ||| % synchronizes the two blocks by unification

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

?X 3 -2 5 0 -1 -3 2 1

?Y 2 1 5 3

!Z * 3 6 8

?X 3 -2 5 0 -1 -3 2 1

?Z * 3 6 8

!V -4 0 -2 -6

V : set of typed variables; v can take value “absent”

State : valuation of V; Transition : pair of states

I : initial condition (set of states)

R : transition relation relating successive states

Run : sequence of R-consistent transitions

Formalizing synchrony

S = (V,I,R)

S ||| S’ = (VUV’,I&I’,R&R’)synch

Formalizing synchrony

S = (V,I,R)

S ||| S’ = (VUV’,I&I’,R&R’)•Alike systems of dynamical equations in maths, but with multiple time-indices

•Perfectly synchronous parallel composition amounts to combining two systems of equations

•No recursion, no dynamical creation, only a single non terminating while loop; body with nested “when”

•Much simpler than Milner’s CCS or Hoare’s CSP

From Synchrony to…

X

Y

V

Asynchrony

X

Y

V

Asynchrony

X

Y

V

Asynchrony

X

Y

V

Asynchrony

X

Y

V Assumes non synchronized,

point to point, re

liable channels

Formalizing Asynchrony

A = (V,)

V : set of typed variables; “absent” meaningless

Flow : sequence of values, for a given variable

Run : tuple of flows

: set of runs

A || A’ = (VUV’, & ’)asynch

Formalizing Asynchrony

A = (V,)

A || A’ = (VUV’, & ’)

A A’Point to point, non

synchronized, channels

Synchrony/Asynchrony

XYV

XYV

?

OK

Some synchronous systems are robust against Asynchronous

environment(a property on infinite runs)

syn

chro

no

us

asynchronous

For these synchronous systems, desynchronization is injective

XYV

XYV

OK

OK

They can be characterized: endochrony

(a property on finite objects)sy

nch

ron

ou

s

asynchronous

Endochrony: example, counterexample

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] |||

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

?X 3 -2 5 0 -1 -3 2 1

?Y 2 1 5 3

!Z * 3 6 8

Endochrony: example, counterexample

loop [ when X>0 then

[get Y ; emit Z=Y+pre(Y)] ] |||

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

?X 3 -2 5 0 -1 -3 2 1

?Z * 3 6 8

!V -4 0 -2 -6

Formalizing endochrony

For W,W’ subsets of V : W W’ iff knowing the value of variables belonging to W determines the status present/absent for all variables of W’

Empty = W0 W1 W2 … Wmax

S is endochronous iff Wmax = V holds

S = (V,I,R)

Endochrony is model-checkable, and can be synthesized

Syn

chro

no

us

exo

chro

no

us

wra

pp

er

A wrapper to enforce endochrony

loop [ when C=1 then present(X,Z)

else when C=2 then present(X)] |||

[ present X then [ present Z then emit U=X+Z else emit V=2X ] ]

end

Some pairs of systems are robust against Asynchronous

communications(a property on infinite runs)

syn

chro

no

us

syn

chro

no

us

asynchronous

They can be characterized: isochrony

(a property on finite objects)sy

nch

ron

ou

s

syn

chro

no

us

asynchronous

Formalizing isochrony

S = (V,I,R) , S ||| S’ = (VUV’,I&I’,R&R’)

R & R’ unify pairs of transitions which agree on the values of their common variables (including status present/absent)

R &w R’ unify pairs of transitions which agree on the values of their common present variables

Isochrony : R & R’ coincides with R &w R’

Syn

chro

no

us

Pairs can be given a wrapper which makes them

isochronous(alike protocol generation)

Syn

chro

no

us

wrap

perw

rap

per

enforce isochrony

GALS architectures as endo/isochronous

networks

iso

endo

Isochrony is compositional

iso

endo

This theory is useful for:

• Generating code, from a synchronous functional architecture, to a GALS architecture

• Handling hybrid synchro/asynchro models at design exploration phase, by performing virtual prototyping

Further issues

• The assumed model of asynchronous communication requires blocking communication: not always acceptable

• Bus infrastructures for distributed control systems are typically non-blocking and time-triggered

Bus for distributed control: loosely synchronized

clocksA small

protocol can emulate our

previous model of

asynchrony

In use, e.g., at Airbus

CONCLUSION

Most of the work presented is due to:

•The community on Synchronous Languages

•ESTEREL (G. Berry,…)

•LUSTRE (P. Caspi, N. Halbwachs,…)

•SIGNAL (P. Le Guernic, A. Benveniste,…)

•The Berkeley community

•PTOLEMY (Ed Lee,…)

•The METROPOLIS project at Cadence (Sangiovanni-Vincentelli,…)

•Supported by vendors (Esterel-Technologies, TNI-Valiosys, and others)

Distributed computing can be

non-high performance

Distributed by the physics; made from

components

Correctness is a major issue

Study models of computation & communication

This is relevant and modern research !!