exploiting user-definable synchronizations in graph transformation

1

Ivan LaneseComputer Science Department

University of BolognaItaly

Exploiting user-definable synchronizationsin graph transformation

Roadmap

Synchronized Hyperedge Replacement

The airport case study

Parametric SHR

Computing a transition step-by-step

Conclusions

Roadmap

Synchronized Hyperedge Replacement

The airport case study

Parametric SHR

Computing a transition step-by-step

Conclusions

Graph transformation

Graphs used to model system structure

– (Hyper)edges are components

– Nodes are communication channels

Graph transformation model system evolution

– Rules replace parts of the graph with new parts

– Captures in an intuitive way reconfiguration

The SHR approach

Traditional graph transformation (e.g., DPO)

requires to match large subgraphs

– Difficult to implement in a distributed setting

The SHR approach

– Rules (productions) describe the behaviour of single

edges

– Productions applied locally

– Synchronization to coordinate different productions

Standard SHR presentation

Algebra to represent graphs

LTS-based semantics

Inference rules to derive transitions from

productions

Apt for developing theory

– Induction on the derivation, coinduction

Difficult to understand

– A transition is a result of many steps of derivation

– Heavy technicalities

Our SHR presentation

Set-theoretical presentation of graphs

LTS-based semantics

Algorithm to derive the allowed transitions

Each step corresponds to an intuitive check

– Choice of the productions, verification of the

synchronization constraints, …

More easy to guess the resulting transitions

More easy to program

More on productions

Rewrite an edge into a graph preserving the

interface

Many productions can be applied concurrently

Synchronization constraints must be satisfied

Mobility can change the interface

at

chk L

at

chkR S

Basics of synchronization & mobility

Productions can execute actions on attached

nodes

Actions executed on each node at each step must

be compatible

Actions can carry nodes as parameters

Parameters of synchronizing actions may be

merged

Synchronization

Mobility

Roadmap

Synchronized Hyperedge Replacement

The airport case study

Parametric SHR• Computing a transition step-by-step • Conclusions

The airport case study

Taken from AGILE project on architectures for

mobility

Models airplanes taking off and landing at airports

and persons traveling using them

Modeled inside AGILE using

– UML extended with mobility primitives

– Synchronized variant of DPO

We concentrate on a small part of the case study

Our aim

univ univ

inBoinBo

chk

chk

inPl

inPl

Programming using productions (1)

at:<req,<newat>>

in:<ε,<>>

chk:<breq,<in>>

newat

in

chk at

at:<ε,<>>

in:<ack,<at>>

at

in

Programming using productions (2)

at:<ε,<>>

chk:<brd,<newat>>

newat

chk at

Idle productions always available

Roadmap

Synchronized Hyperedge Replacement

The airport case study

Parametric SHR

Computing a transition step-by-step

Conclusions

Parametric SHR

A member of SHR family

Synchronization and mobility patterns not fixed but

user-definable

– Specified using Synchronization Algebras with Mobility

Allows to use each time the most suitable

synchronization primitives

Synchronization Algebras with Mobility

Specify how actions synchronize– Two at the time, associativity and commutativity required

From Winskel’s synchronization algebras– Partial operator ● for action synchronization

– Action ε for “not taking part to the synchronization”

Added– Arities of actions

– Function from parameters of the synchronizing actions to

parameters of the result

– Set of final actions

Milner SAM

Normal actions, coactions, τ, ε

in ● out = τ

a ● ε = a

Final actions: τ, ε

in out τ

a ε a

Broadcast SAM

Normal actions, coactions, ε

in ● out = out

in ● in = in

ε ● ε = ε

Final actions: out, ε

in out out

in in in

And many more

SAMs can be defined for many synchronization

policies

– Mutual exclusion

– Priority synchronization

– …

SAMs can be combined

– In the example: req and acq interacting using Milner

synchronization and breq and brd interacting using

broadcast

Applying a SAM

SAMs used to synchronize tuples of actions a i

carrying parameters pi

If synchronization is allowed we can compute

– A resulting action c

– A substitution σ

– A tuple of parameters p

Applying broadcast

Broadcast synchronization is allowed if – at most one action is “out”

– if there is an ε, then all the actions are ε

The result is – ε if all actions are ε

– “in” if all the actions are “in” (not allowed on bound nodes)

– “out” otherwise

Substitution σ computed as mgu of equalities pi=pj for all i, j

Parameters p computed as piσ (any i can be chosen)

Roadmap

Synchronized Hyperedge Replacement

The airport case study

Parametric SHR

Computing a transition step-by-step

Conclusions

The algorithm (1)

One production is chosen for each edge

– Idle production for passenger not checked in

– Productions shown before for other edges

– New nodes are local to productions

The actions executed on each node x are

synchronized

– Action cx, parameters px and substitution σx as results

If x is bound then cx must be final

Synchronization in the example

univ

inBo

chk

inPl

ε,<>

ack,<univ>ε,<>ε,<>

ε,<>req,<newat>

ε,<>

breq,<inPl>brd,<new1>

brd,<new2>

Synchronization in the example

univ

inBo

chk

inPl

ε

τ

ε

breq,<inPl>brd,<new1>

brd,<new2>

univ/newat

Synchronization in the example

univ

inBo

chk

inPl

ε

τ

ε

breq,<inPl>

univ/newat

inPl/new1,inPl/new2

The algorithm (2)

Global substitution σ computed by

– Merging the substitutions σx from single nodes

Final label contain

– The triple <x, cx, pxσ> for each free x in the LHS

Final graph computed by– Merging the RHSs of the productions

– Applying the global substitution σ

– Hiding nodes unless free in the LHSs or occurring in the label

– Deleting isolated nodes

Result of the transition

univ

inBo

newat

inPl

chk

new1 new2

univ/newat, inPl/new1, inPl/new2

Result of the transition

univ

inBoinPl

chk

univ/newat, inPl/new1, inPl/new2

Result of the transition

univ

inBoinPl

chk

The label is <x,ε,<>>

Result of the transition

univ

inBoinPl

chk

All nodes but univ are hidden

Roadmap

Synchronized Hyperedge Replacement

The airport case study

Parametric SHR

Computing a transition step-by-step

Conclusions

Conclusions

About SHR– Powerful graph transformation framework

– Allows to relate local and global views of the system

About PSHR– Allows to simplify the specification of complex transformations

About this presentation of PSHR– Less suitable for developing theory

– Hopefully more apt for designers/developers

– The two views are (nearly) equivalent: the most suitable can be

chosen at each time

Future work

I have moved, so I’m not sure I will continue

working on this

Some interesting things on SHR under

development

– Category of SAMs to compose and compare them

– Applying SHR to QoS

– Abstract semantics for SHR

One thing that is surely missing

– Implementation of SHR

End of talk