Synchronization strategies for global computing models

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Ivan LaneseComputer Science Department

University of Bologna

Synchronization strategiesfor global computing models

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Roadmap

Global computing

Synchronized Hyperedge Replacement

SHR vs Fusion Calculus

Synchronization Algebras with Mobility

Congruence results

Future work

3

Roadmap

Global computing




Congruence results

Future work

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What is global computing?

Essentially networks

deployed on huge areas

Global computing

systems quite common

nowadays

– Internet, wireless

communication networks,

overlay networks …

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Features of global computing systems

Distribution

– Huge areas: localities can not always be hidden

Mobility

– Both physical and code mobility

Heterogeneity

– Interoperability, coordination

Openness

Reconfigurability

Non-functional requirements

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Formal methods for GC

Building models of the system

– To concentrate on a particular aspect

– To abstract from details

– To analyze the properties of the system before building it

Traditional formal methods are not enough for GC

– Mobility must be modeled explicitly

– Need for compositionality

– Need for more abstraction

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High level models

We look for models at the high level of abstraction

– Models of coordination among subsystems

We need powerful primitives

– Multiple synchronizations

– Abstractions of full protocols

Declarative specification of constraints

– Possible evolutions derived as solution of system of

constraints

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Roadmap

Global computing




Congruence results

Future work

9


A graph transformation approach

– Suitable to deal with distribution, mobility, compositionality

(Hyper)edges are systems connected through common nodes

Productions describe the evolution of single edges

– Local effect, easy to implement

Synchronization via constraints on nodes

– Determines which productions can be applied concurrently

– Productions applied indipendently

– Allows to define complex transformations

– Multiple synchronization is allowed

Declarative approach

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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

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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

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Synchronizing productions

Synchronization: productions execute actions

on nodes. A transition is allowed iff the

synchronization constraints imposed on actions are

satisfied

Many synchronization models are possible

(Hoare, Milner, ...)

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An example: Milner SHR

Milner synchronization: pair of edges can synchronize by performing complementary actions

a

A1

aA1 B1

a

A2

a

B1 B2

A2 B2

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SHR with mobility

– Actions carry tuples of references to nodes (new or already

existent)

– References associated to synchronized actions are matched and

corresponding nodes are merged

We use name mobility

a<x>

A1

a<x>A1 B1

a<y>

A2

a<y>

B1 B2

A2 B2

x y

x=y

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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)

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Algebraic presentation of SHR

Graphs represented as terms

– Edges (applied to nodes) are basic constants

– Operators for parallel composition and hiding of

nodes

Transitions described by a LTS

Inference rules to derive transitions from

productions

Allows proofs by induction

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Roadmap

Global computing




Congruence results

Future work

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Fusion Calculus

Calculus for mobility inspired by π-calculus

Input prefix is not a binder

– Symmetric input/output

– Names are merged

– Input of π-calculus obtained as input+restriction on

the objects of the input

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Many common features

– LTS semantics

– Synchronization in Milner style

– Mobility using fusions

Straightforward mapping of Fusion into SHR

SHR adds:

– Graphical presentation

– Multiple synchronizations

– Concurrent semantics

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Fusion Calculus vs SHR

Fusion Milner SHR

Processes Graphs

Sequential processes Hyperedges

Names Nodes

Parallel comp. Parallel comp.

Scope Restriction

Prefixes Productions

Transitions Interleaving tr.

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Example

).|.|.)(( RzyQyxPuxxy

)||)((

).|.|)(().|.|.)(( )(

RQPy

RzyQyxPyRzyQyxPuxxyzx

uxx

We can also execute both the steps at the same time

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Roadmap

Global computing




Congruence results

Future work

23

Synchronization Algebras with Mobility (1)

Extend Winskel’s synchronization algebras to deal with name

mobility and local resources

Allow to have synchronization models as first-class citizens– Can be used to have models with parametric synchronization policies

– Many synchronization policies in the same model

– Different policies can be compared and combined

Common policies can be expressed as SAMs– Simple ones: Milner, Hoare, broadcast

– More complex ones: with priority, treshold synchronization

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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

– Final actions (performed on local channels)

– Some more technical stuff

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Milner synchronization as a SAM

Actions: normal actions, coactions, τ, ε

ε stands for “not taking part to the synchronization”

Normal actions synchronize with corresponding

coactions giving τ, corresponding parameters are

fused, no parameters are propagated

Anything can synchronize with ε, action and

parameters are propagated, no fusions

No other synchronization is allowed

Only τ and ε can be performed on local channels

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Sample synchronization

a b c

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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 in general

– Allows to highlight relations between properties of

SAMs and properties of the model

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Heterogeneous SHR

Allows to model heterogeneous systems

– Different primitives in different parts of the system

– Example: wireless connections with broadcast and

wired connections with Milner

Each node is labeled by a SAM

SAMs must be managed dynamically

– SAMs are required to form a commutative monoid

– Node fusions cause SAMs composition

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PRISMA Calculus

Generalization of Fusion based on SAMs

– Prefixes of the form x a y . P

– Synchronization ruled by the SAM

Standard Fusion is (more or less) Milner

PRISMA Calculus

The same approach can be applied to other

calculi (with some more technical difficulties)

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Roadmap

Global computing




Congruence results

Future work

32

Abstract semantics for parametric SHR

Bisimulation can be defined in a standard

way for SHR

Under reasonable conditions on the SAM

bisimilarity is a congruence for parametric

SHR

– Milner, Hoare and many others satisfy the

conditions

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Congruence results for Fusion Calculus

Bisimilarity is not a congruence for Fusion

Calculus (not closed under substitutions)

The mapping from Fusion into SHR allows to

derive a semantics whose bisimilarity is a

congruence

The result can be extended also to π-calculus

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The idea of the semantics

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The idea of the semantics

Allowing many actions in the same transition but on

different channels

– Process a|b can execute a and b concurrently going to 0

(but can also execute either a or b)

– Process a|a is bisimilar to a.a

– Process a|a|b can perform τ and b concurrently going to 0

Allows to observe the degree of parallelism of a

process

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Congruence properties

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no more a counterexample since the

two terms are not bisimilar

b|a.abba.

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no more a counterexample since the

two terms are not bisimilar

Observing where a synchronization is performed

becomes important

– Otherwise congruence non preserved by context a|[-]

– Actions aτ in addition to normal τ

The resulting bisimilarity is a congruence

b|a.abba.

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Roadmap

Global computing




Congruence results

Future work

40

Future work

I have moved, so my work has changed a bit

– Core calculus for service oriented computing

– Techniques for proving bisimilarity properties of mobile calculi

Some follow-up of the previous work that I would like

to analyze

– Congruence results for concurrent semantics of π-calculus

– Applying SAMs to π-calculus

– Exploiting SAMs for quality of service (see Tuosto & Hirsch

work)

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General bibliography

“A Model of Distributed Systems based on Graph Rewriting”, P.

Degano and U. Montanari, Journal of the ACM, 34

““Synchronized Hyperedge Replacement with Name Mobility”, D. Synchronized Hyperedge Replacement with Name Mobility”, D.

Hirsch and U. Montanari, Proceedings of CONCUR 2001, LNCS Hirsch and U. Montanari, Proceedings of CONCUR 2001, LNCS

21542154

“The Fusion Calculus: Expressiveness and Symmetry in Mobile

Processes”, B. Victor, Ph.D. Thesis, Department of Computer

Systems, Uppsala University, Uppsala, Sweden

“Synchronization trees”, G. Winskel, TCS, 34

“SHReQ: Coordinating Application Level QoS”, D. Hirsch and E.

Tuosto, Proceedings of SEFM 2005, IEEE

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My bibliography

“Software Architecture, Global Computing and Graph Transformation via

Horn Clauses”, I. Lanese and U. Montanari, Proceedings of SBES 2002 –

16th Brazilian Symposium on Software Engineering

“A Graphical Fusion Calculus”, I. Lanese and U. Montanari, Proceedings of

CoMeta: Computational Metamodels Final Workshop, ENTCS 104

“Mapping Fusion and Synchronized Hyperedge Replacement into Logic

Programming”, I. Lanese and U. Montanari, to appear in a special issue of

TPLP

“Synchronization Algebras with Mobility for Graph Transformations”, I.

Lanese and U. Montanari, Proceedings of FGUC 2004 – Workshop on

Foundations of Global Ubiquitous Computing, ENTCS 138

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My bibliography

“Synchronized Hyperedge Replacement for Heterogeneus Systems”, I.

Lanese and E. Tuosto, Proceedings of COORDINATION 2005, LNCS 3454

"Hoare vs Milner: Comparing Synchronizations in a Graphical Framework

with Mobility", I. Lanese and U. Montanari, Proceedings of GT-VC‘05,

ENTCS, to appear

"Exploiting User-Definable Synchronizations in Graph Transformation",

I. Lanese, Proceedings of GT-VMT'06, ENTCS, to appear

"Synchronization Strategies for Global Computing Models",

Ivan Lanese, Ph.D. Thesis, Computer Science Department, University of

Pisa, to appear

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End of talk

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Synchronization strategies for global computing models