1 Ivan Lanese Computer Science Department University of Pisa (moved to Bologna) Synchronization...

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Ivan LaneseComputer Science Department

University of Pisa(moved to Bologna)

Synchronization strategiesfor global computing models

Ph.D. thesis discussion

Supervisor: prof. Ugo Montanari

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Roadmap

Global computing

Comparing models for GC

Parametric synchronizations with mobility

Observational semantics and compositionality

Conclusions

3

Roadmap

Global computing




Conclusions

4

What is global computing?

Essentially networks

deployed on huge areas

Global computing

systems quite common

nowadays

– Internet, wireless

communication networks,

overlay networks …

5

Features of global computing systems

Distribution

– Localities may have a semantic meaning

Heterogeneity

– Interoperability, coordination

Mobility

Openness

Reconfigurability

Non-functional requirements

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Formal methods for GC

Building models of the system

Old aims

– Concentrate on a particular aspect

– Abstract from details

– Analyze the properties of the system before building it

But new approaches/tools must be used

– Mobility and non-functional requirements must be modeled

explicitly

– Need for compositionality

– Need for more abstraction

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High level models

Models of coordination among components

Components interact via interfaces

Declarative specification of synchronization constraints– Possible evolutions derived as solution of system of constraints

Single components may be complex

We need powerful primitives– Multiple synchronizations

– Abstractions of full protocols

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Roadmap

Global computing




Conclusions

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Why comparing models?

Different models for GC exist

– Process calculi, graphs, UML, categorical models…

Each model has strengths and weaknesses

Compare models to

– Find strengths and weaknesses

– Combine the strengths

– Categorize them

– Move some steps toward a (maybe) unique model

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Which comparisons?

N models → 2N comparisons

Must select some representatives

– Show at a first sight some interesting connections

We have chosen

– Logic programming

– A graph transformation framework: SHR

– A process calculus: Fusion Calculus

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Logic programming

Traditionally language for AI and problem

solving

In the GC scenario seen as goal rewriting

framework

Unification as synchronization primitive

Focus on partial computations

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Long background on SHR

NOOO!!!

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Very short background on SHR

Graph transformation formalism

Productions specify the behaviour of edges

Synchronization via actions on common nodes

– Hoare, Milner

Mobility by creating, sending and merging

nodes

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Fusion Calculus

Calculus for mobility inspired by π-calculus

Input prefix is not a binder

– When input and output interact a name fusion is generated

– The scope of the fusion is determined by an explicit scope

operator

Symmetric input/output

Arbitrary fusions allowed

Input of π-calculus obtained as input+scope

– Not fully abstract since more powerful contexts are available

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Hoare SHR vs logic programming

Hoare synchronization strictly related to unification

Strong relation between Hoare SHR and

Synchronized Logic Programming

– A subset of logic programming

– No nested functions

– Transactional application of many clauses

– Exploits function symbols for synchronization» Similar to tokens in zero-places of zero-safe nets

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Summary of the comparison

Hoare SHR SLP

Graph Goal

Hyperedge Atom

Node Variable

Parallel comp. AND comp.

Action Function sym.

Production Clause

Transition Transaction

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An example

y

C

x

y

C

z

C

x

y

C

x

y

S

xr<w>

r<w>

w

C(x,y)←C(x,z),C(z,y)

C(r(x,w),r(y,w))←S(y,w)

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Dynamics

x C

C

C

C

C

C

C

CC C

S

S

SS

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Dynamics

x C

C

C

C

C

C

C

CC C

S

S

SS

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Main results

Simple (homomorphic) mapping

Complete correspondance

Suggests how to introduce restriction in logic

programming

What about Milner logic programming?

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Milner SHR vs Fusion Calculus

Many common features

– Synchronization in Milner style

– Mobility using fusions

– LTS semantics

Straightforward mapping of Fusion into Milner SHR

SHR adds:

– Graphical presentation

– Multiple synchronizations

– Concurrent semantics

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Summary of the comparison

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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Main results

Simple (homomorphic) mapping

Complete correspondance

Suggests many generalizations of Fusion

– A concurrent semantics

– PRISMA Calculus

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Milner vs Hoare

Surprisingly the most difficult step

Simulating Hoare using Milner

– Must implement n-ary synchronization using binary

synchronization

Simulating Milner using Hoare

– Milner synchronization is asymmetric

– In Milner restriction affects the behaviour, in Hoare

just the observation

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Some results

Not equivalent in general

In closed 2-shared graphs Milner is more powerful than Hoare– Hoare implemented by dropping the distinction between actions and

coactions

A translation of graphs can be used to bridge the gap in many

cases– Amoeboids to simulate synchronization

Hoare amoeboids are broadcasters

Milner amoeboids are routers– Mutual exclusion can not be enforced

– Not a problem in 2-shared graphs

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And so?

Synchronization and mobility strategies are an

important characteristic of a model

Difficult to simulate a strategy using another

one

Have strategies as parameters of the system

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Roadmap

Global computing




Conclusions

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Synchronization Algebras with Mobility (1)

Extend Winskel’s synchronization algebras to deal with name

mobility and local resources

Allow to have synchronization strategies 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

– Arities for actions

– Mapping from parameters of synchronizing actions to

parameters of the result

– Fusions among parameters

– Final actions (can be performed on local channels)

– Some more technical stuff

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Sample synchronization

a b c

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Milner SAM

Normal actions, coactions, τ, ε

(in, out, τ)

(a, ε, a)

Final actions: τ, ε

a ε a

in out τ

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Combining SAMs

SAMs form a category

Standard constructions can be used to

compose SAMs

– Coproduct makes different protocols available

– Product applies two protocols in parallel

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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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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

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Take-off transition

univ univ

inBoinBo

chk

chk

inPl

inPl

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Specifying the transition (1)

at:<req,<newat>>

in:<ε,<>>

chk:<breq,<in>>

newat

in

chk at

at:<ε,<>>

in:<ack,<at>>

at

in

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Specifying the transition (2)

at:<ε,<>>

chk:<brd,<newat>>

newat

chk at

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Synchronization in the example

univ

inBo

chk

inPl

ε,<>

ack,<univ>ε,<>ε,<>

ε,<>req,<newat>

ε,<>

breq,<inPl>brd,<new1>

brd,<new2>

Can be obtained using as SAM

the coproduct of:

● Milner SAM for req and ack

● Broadcast SAM for breq and brd

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Effects of the synchronization

univ

inBo

chk

inPl

ε

τ

ε

breq,<inPl>

univ/newat

inPl/new1,inPl/new2

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Result of the transition

univ

inBoinPl

chk

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Heterogeneous SHR

Allows to use different SAMs on different nodes

Concentrates on dynamic management of SAMs

– SAMs are required to form a commutative monoid

– Node fusions cause SAM composition

Allows to model heterogeneous systems

– Different primitives in different parts of the system

– Example: wireless connections with broadcast and wired

connections with Milner

Conservative extension of parametric SHR

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A network example

Network with routers and clients Channels can have

– 4Kb/16Kb packets

– Error detection/no error detection

To communicate a client creates a virtual communication channel that uses the underlying infrastructure

The communication channel supports 16Kb packets/error detection only if all the underlying channels do

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Modeling the scenario

Eight different SAMs with all the combinations of– 4Kb < 16Kb

– No error detection < error detection

– Communication < control

SAMs provide variants of Milner synchronization– E.g. action for detecting errors

SAMs form a partial order (pointwise) SAM composition corresponds to glb

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Building a virtual channel

CR R

C R R

16,√ 4,×

16,×

4,√16,√

16,×

4,√

comm,16,×

Act

Act

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Ideas on the derivation

Each production poses some constraints on the features of the resulting channel

During synchronization the constraints are composed according to the specified pattern

The characteristics of the resulting channel are automatically computed

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PRISMA Calculus

SAM-based process calculus

– Prefixes of the form x a y . P

– Synchronization ruled by the SAM

– Mobility using fusions

– Standard operators can be included

Milner PRISMA Calculus is (essentially) Fusion

Calculus

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Hints on technical difficulties

In some SAMs (e.g., Hoare) a set of processes

must interact to allow a synchronization on x

– All the processes

– All the processes that know x

– All the processes able to synchronize on x

We have chosen the last approach

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Roadmap

Global computing




Conclusions

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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

Proof exploits bialgebraic techniques

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Congruence results for Fusion Calculus

Bisimilarity is not a congruence for Fusion

Calculus (not closed under substitutions)

The comparison with SHR shows why it fails

and suggests how to solve the problem

We have proposed a new concurrent

semantics

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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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Observational semantics of PRISMA

Hyperbisimilarity is a congruence

Common axioms bisimulate for each SAM

A translation along a morphism can be used to

change the used SAM

Translations along isomorphisms preserve

bisimilarity

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Roadmap

Global computing




Conclusions

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Conclusions on SHR

SHR is an interesting model for GC

– Deals well with distribution, synchronization,

mobility

– Can be extended to deal with eterogeneity

– Good compositionality features have been proved

– Some extensions for dealing with non-functional

requirements are under analysis [Hirsch & Tuosto]

Strong connections with process calculi

– Allow cross-fertilization

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Conclusions on synchronization models

Synchronization and mobility patterns are a

dimension in the space of GC models

– Can be factored out

Parametric models help modeling phase

Different SAMs can

– be composed

– interoperate

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Conclusions on compositionality

General and original result on compositionality for

graph transformations

Interesting result for Fusion Calculus

– Connection between concurrency and compositionality

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Future work

Further analysis required in many directions

Exploiting the mappings for cross-fertilization

Comparing SHR with other graph transformation

frameworks

Analyzing the properties of the new models

Moving from Fusion towards π-calculus

Techniques for proving compositionality

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Future work



– Milner logic programming

– Multiple synchronizations in process calculi


frameworks




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Future work




frameworks

– DPO

– Bigraphs




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Future work




frameworks


– Concurrent Fusion

– PRISMA Calculus



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Future work




frameworks



– Concurrent π-calculus

– Parametric π-calculus


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Future work




frameworks




– Bialgebraic techniques requires complex semantics

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Bibliography of the thesis

“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, TPLP, special issue, to appear

“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

“Insights Emerged while Comparing Three Models for Global Computing”, I. Lanese

and U. Montanari, Proceedings of Dagstuhl seminar 05081 on Foundations of

Global Computing, Electronic proceedings, 2005

“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

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Other publications

“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

“On Graph(ic) Encodings”, R. Bruni and I. Lanese, Proceedings of Dagstuhl seminar

04241 on Graph transformations and process algebras for modeling distributed and

mobile systems, Electronic proceedings, 2004

“New Insights on Architectural Connectors”, R. Bruni, J. Fiadeiro, I. Lanese, A.

Lopes and U. Montanari, Proceedings of IFIP TCS’04, Kluwer

“Complete Axioms for Stateless Connectors”, R. Bruni, I. Lanese and U. Montanari,

Proceedings of CALCO’05, LNCS 3629

“A Basic Algebra of Stateless Connectors”, R. Bruni, I. Lanese and U. Montanari,

TCS, to appear

"Exploiting User-Definable Synchronizations in Graph Transformation",

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

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1 Ivan Lanese Computer Science Department University of Pisa (moved to Bologna) Synchronization...

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