1
Synchronization strategiesfor global computing models
Ivan LaneseComputer Science Department
University of Bologna
2
Roadmap
Application field: global computing
The main tool: graphs and SHR
Some contributions
– Parametric synchronization
– Compositionality properties
– Relations with Fusion Calculus
And after?
3
What is global computing?
Essentially networks
deployed on huge areas
Global computing
systems quite common
nowadays
– Internet, wireless
communication networks,
…
4
Challenges of global computing systems
Distribution, mobility, heterogeneity, openness,
reconfigurability, non-functional requirements
Traditional formal methods are not enough
– Strong emphasis on coordination among
subsystems
– Mobility must be modeled explicitly
– Need for compositionality and high abstraction
5
Synchronized Hyperedge Replacement
We want to model systems as graphs
Components are edges
Links are common nodes
Behaviour specified by transitions
– Derived from the behaviour (productions) of single components
– Keep into account synchronization and communication/mobility
6
Hyperedge Replacement Systems
A production describes how the hyperedge L is rewritten into the graph R
R
1
2 3 4
L
1
2 3 4 H
7
Hyperedge Replacement Systems
A production describes how the hyperedge L is transformed into the graph R
R
R’
1
2 3 4
1
2
3
Many concurrent rewritings are allowed
L
L’
1
2 3 4
1
2
3
H
8
Synchronizing productions
Synchronization: productions execute actions
on nodes. Actions on the same node should be
compatible
Two existing synchronization models: Milner
(message passing) and Hoare (agreement)
9
Milner SHR
Milner synchronization: pair of edges can synchronize by performing complementary actions
a
A1
aA1 B1
a
A2
a
B1 B2
A2 B2
10
SHR with mobility
– Actions carry references to nodes
– References associated to synchronized actions are matched and
corresponding nodes are merged
We use node mobility
a<x>
A1
a<x>A1 B1
a<y>
A2
a<y>
B1 B2
A2 B2
x y
x=y
11
Example
x
Initial Graph
C
Brother:
C
C
C
C S
Star Reconfiguration:
w
r<w>
r<w>
x CBrother
C
C
C
C
C
C
CC CBrother Brother
(4)(3)(2)(1)
Star Rec.S
S
SS
(5)
12
Algebraic presentation of SHR
Helps the development of the theory
– Proofs by induction
Graphs represented as terms in an algebra
– Edges are basic constants
– Operators for composing them
Transitions described by a labelled transition system
Inference rules to derive transitions from productions
13
Parametric synchronization
The expressive powers of Hoare and Milner
synchronizations are not comparable
– Can specify different classes of reconfigurations
Is it possible to find some more general framework?
Winskel proposed synchronization algebras to
describe general synchronizations
– Not suitable for synchronizations with mobility
We generalize them to SAMs (Synchronization
Algebras with Mobility)
15
Synchronization Algebras with Mobility
SAs specify composition of actions
– (a,a,τ) a synchronizes with a producing τ
SAMs also provide
– Mapping from parameters of synchronizing actions
to parameters of the result
– Fusions among parameters
– Some more technical stuff
17
Parametric SHR
The SAM is a parameter of the model
Different models obtained via instantiation
– Allows to recover Hoare and Milner SHR…
– …and to easily define new models
Properties can be proved for any SAM or for a
class of SAMs
Many SAMs can be used in the same model
– Useful to model heterogeneous systems
18
Compositionality for parametric SHR
Bisimulation allows to observe interactions
of a system with the environment
– Can be defined in a standard way for SHR
Bisimulation is a congruence for SHR with
most SAMs
– Behaviour of a system can be inferred from the
behaviour of its components
19
Fusion Calculus
Calculi for mobility allow to model concurrent
and mobile systems
– π-calculus is the most used
Fusion Calculus generalizes and simplifies it
– More symmetric
– Shared-state update
20
Milner SHR vs Fusion Calculus
Apparently very different models
Some important similarities
– Synchronization in Milner style
– Mobility using fusions
Faithful mapping of Fusion into Milner SHR
SHR is more general
– Graphical presentation
– Multiple synchronizations
– Concurrent semantics
21
Fusion Calculus vs Milner SHR
Fusion Milner SHR
Processes Graphs
Sequential processes Hyperedges
Names Nodes
Comm. primitives Productions
Transitions Interleaving tr.
23
Exploitation of the mapping
The results obtained for SHR can be applied to
Fusion Calculus
PRISMA Calculus = Fusion + SAMs
The semantics of Fusion induced by the
mapping is compositional
– The result does not hold for the standard semantics
– The trick is concurrency
24
Future work
Some applications to π-calculus
– Analysis of the concurrent semantics of π-calculus
– Application of SAMs to π-calculus
From global computing to service oriented computing
– In service oriented computing services are discovered, invoked and composed
– Which are the correct primitives to model them?
– Which are the interesting properties and equivalences?