Exploiting user-definable synchronizations
in graph transformation
Ivan Lanese
Computer Science Department
University of Bologna
Italy
1
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
at
at
chk
L
chk
R

Many productions can be applied concurrently

Synchronization constraints must be satisfied

Mobility can change the interface
S
Basics of synchronization & mobility

Productions can execute actions on attached
nodes

Actions executed on each node at each step must
be compatible
Synchronization

Actions can carry nodes as parameters

Parameters of synchronizing actions may be
merged
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
chk
inPl
inBo
inBo
chk
inPl
Programming using productions (1)
at:<ε,<>>
at
in:<ack,<at>>
in
at:<req,<newat>>
chk:
<breq,<in>>
newat
at
chk
in:<ε,<>>
in
Programming using productions (2)
at:<ε,<>>
chk:
<brd,<newat>>
newat
chk
Idle productions always available
at
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
out
out
in
in
in

in ● in = in

ε●ε=ε

Final actions: out, ε
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 ai
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
ε,<>
univ
ack,<univ>
inBo
ε,<>
ε,<>
req,<newat>
ε,<>
brd,<new1
breq,<inPl>
>
chk
ε,<>
brd,<new2
>
inPl
Synchronization in the example
ε
univ
inBo
univ/newat τ
ε
inPl
brd,<new1
breq,<inPl>
>
chk
brd,<new2
>
Synchronization in the example
ε
univ
inBo
univ/newat τ
ε
inPl
breq,<inPl>
chk
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
newat
chk
inBo
inPl
new1
univ/newat, inPl/new1, inPl/new2
new2
Result of the transition
univ
chk
inBo
univ/newat, inPl/new1, inPl/new2
inPl
Result of the transition
univ
chk
inBo
The label is <x,ε,<>>
inPl
Result of the transition
univ
chk
inBo
All nodes but univ are hidden
inPl
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