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Ivan LaneseComputer Science Department

University of Pisa

Prof. Ugo Montanari

Synchronization strategiesfor global computing

Relator:

Thesis Progress Report

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Roadmap

Global computing

SHR and other formal tools

What we did in the first year

What we planned after the first year

What we have done

What is still to be done

3

Roadmap

Global computing

SHR and other formal tools

What we did in the first year

What we planned after the first year

What we have done

What is still to be done

4

What is global computing?

Essentially networks

deployed on huge areas

It is becoming the most

widespread computing

paradigm

– 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

Eterogeneity

– Interoperability, coordination

Openness

Reconfigurability

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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 high level of abstraction

– Models of coordination among subsystems

– For making the model of the whole system treatable

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

SHR and other formal tools

What we did in the first year

What we planned after the first year

What we have done

What is still to be done

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Synchronized Hyperedge Replacement

Follows the traditional approach of graph transformation– Deals well 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

– Global constraint solving algorithm to find allowed transitions

– Productions applied indipendently

– Allows to define complex transformations

– Allows multiple synchronization

– 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

Synchronized transitions: we associate

actions to 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 doing complementary actions

a

3 3

B1 A1

B2 A2

aa a

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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>B1 A1

B2 A2

a<y>a<x>a<y>

(x) (y)x=y

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Other formal tools: CommUnity in one slide

Architectural model of concurrent systems

Based on communication via channels and

synchronization of actions

Separation between computation and coordination

concerns

– Computation inside programs

– Coordination explicitly represented via morphisms and

special programs (cables)

– Composition via colimits

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Other formal tools: Tile Model in one slide

Extension of SOS systems and rewriting logic

that allows synchronization

– Rules have trigger and effect

Operators of horizontal, vertical and monoidal

composition

Useful for studying observational properties of

open systems

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Roadmap

Global computing

SHR and other formal tools

What we did in the first year

What we planned after the first year

What we have done

What is still to be done

old

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Comparing models for GC

Comparing synchronization strategies, mobility strategies and

binding operators in different models

Comparative analysis of the following paradigms– Fusion Calculus: calculus for mobility, allows fusions

– SHR: already presented in detail

– Logic programming: developed programming paradigm, we use it as

goal rewriting mechanism, to be extended to deal with GC systems

Mapping of Fusion Calculus into SHR and of SHR into logic

programming– Fusion Calculus is a subset of Milner SHR

– Logic programming (with transactions) related to Hoare SHR

old

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Comparing strategies for compositionality Two approaches to compositionality

– Categorical approach: via universal constructions

(colimits)

– Algebraic approach: via operators for building

systems

Our case study: CommUnity vs Tile Model

old

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Results from CommUnity vs tiles

Semantics for CommUnity

Decomposition of CommUnity programs

New algebra of connectors (in the Tile Model)

that simulates CommUnity synchronization

Correlation between colimit and algebraic

aspects (bisimulation, axiomatization)

old

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Roadmap

Global computing

SHR and other formal tools

What we did in the first year

What we planned after the first year

What we have done

What is still to be done

plan

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A physical analogy

Physical systems– Many interacting components

– Partial derivative equations for parts of the space

– Components of the system gives boundary conditions

– The solutions of the system of equations are the allowed behaviors

Global computing systems– Equations associated to the interfaces

– Equations are a declarative way of specifying coordination

– Only simple equations used in past works

» Hoare and Milner synchronization in SHR

Developing new models using this analogy

plan

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Different items

Extending synchronization algebras with mobility– Standard synchronization algebras allow to categorize

synchronization models

– Need extensions to be applied to GC models

– SHR well-suited for these analysis

Analyzing observational semantics of GC models– Allows to analyze incomplete systems (compositionality)

– Tile Logic well-suited for such analysis

Hybrid models– For taking the best features of different models

– Suggested by the comparisons done

plan

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General aim

Double aim:

– Analyzing existing models and their relationships

– Looking for new models for GC systems

plan

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Roadmap

Global computing

SHR and other formal tools

What we did in the first year

What we planned after the first year

What we have done

What is still to be done

ok

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SAMs (1)

Synchronization algebras with mobility

– Extend synchronization algebras to deal with name

mobility and local resources

– Different synchronization policies allowed

» Simple ones: Milner, Hoare, broadcast

» More complex ones: with priority, treshold

synchronization

– Like differential equations for physics

ok

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SAMs (2)

SAs specify composition of actions

SAMs also gives:

– Mapping from parameters of synchronizing actions

and parameters of the result

– Fusions among parameters

– Final actions (performed on local channels)

– Some more technical stuff

ok

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An example: SAM for Milner synchronization

Actions: normal actions, coactions, tau, epsilon

Normal actions synchronize with corresponding

coactions giving tau, corresponding parameters are

fused, no parameters are propagated

Anything synchronize with epsilon, action and

parameters are propagated, no fusions

No other synchronization is allowed

Only tau and epsilon can be done on local channels

ok

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Applying SAMs

Applied in the context of SHR

Parametric SHR– The SAM is a parameter of the model

– Different models obtained via instantiation

– Properties can be proved in general

Heterogeneous SHR– Each node is labelled by a SAM

– SAMs are required to form a commutative monoid

– Node fusions cause SAMs composition

Broadcast fusion calculus– Via the mapping discovered in the first year

ok

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Abstract semantics for SHR

Bisimulation for (parametric) SHR

Congruence results w.r.t. a suitable algebra

of graphs

Found using the Tile Model as framework,

but then provable indipendently

ok

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Extending CommUnity vs Tile Model (1)

Analysis of the class of connectors for

CommUnity– 3 different semantics for connectors

» observational

» axiomatic

» denotational

– The 3 semantics are equivalent

– Study of the expressivity of different

classes of connectors

– The larger class allows to produce a

connector for each denotation

ticktick

tick

;; idid

∆ 0 100 tick untick01 untick untick10 untick untick11 untick tick

ok

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Extending CommUnity vs Tile Model (2)

Double correspondance between

categorical and algebraic approach

– Starting diagram and colimit equals up to

bisimulation

– Axiomatization of bisimulation and reduction

to normal form allow to compute colimit

algebraically

ok

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Roadmap

Global computing

SHR and other formal tools

What we did in the first year

What we planned after the first year

What we have done

What is still to be done

todo

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From planned work

More refined abstract semantics

– Abstract semantics for SHR is very (too) distinguishing

Hybrid models

– Models with different synchronization policies have been

derived but their properties have to be analyzed in more

depth

– What about other hybrid models?

SAMs

– SAMs have been applied to SHR

– Can them be applied to other formalisms (process-calculi)?

todo

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New ideas

Refining

– To bridge the gap between high level models and

implementation

– Must preserve behavioral properties

Combining SHR and bigraphs

– Bigraphs and SHR have the same field of

application but different aim (double structure vs

compositionality)

todo

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Bibliography (old)

“Software Architecture, Global Computing and Graph

Transformation via Horn Clauses”, I. Lanese and U. Montanari,

Proceedings 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, under

review for publication in a special issue of TPLP

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Bibliography (new)

“Synchronization algebras with mobility for graph

transformations”, I. Lanese and U. Montanari, Proceedings

FGUC 2004, ENTCS, to appear

“Synchronized Hyperedge Replacement for heterogeneus

systems”, I. Lanese and E. Tuosto, submitted to

COORDINATION 2005

“New insights on architectural connectors”, R. Bruni, J.L.

Fiadeiro, I. Lanese, A. Lopes and U. Montanari, Proceedings

IFIP TCS 2004, Kluwer Academics

“Normal forms for stateless connectors”, R. Bruni, I. Lanese

and U. Montanari, submitted to CALCO 2005

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End of talk

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Observational and abstract semantics

Analyzing observational and abstract

semantics of models

– Useful for abstracting details

– Important to analyze relationships with

compositionality

Tile Model is well suited for this kind of

analysis

– Existing criteria for compositionality too

restrictive for GC applications

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Hybrid models

Plugging features from a model into another one

Expressiveness and properties of new models must

be analyzed

Ongoing work:

– Logic programming with restriction

– Concurrent Fusion Calculus

New ideas:

– Non Milner Fusion Calculus

– Non Hoare logic programming

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Algebra of synchronization strategies

Synchronization algebras

– Categorize synchronization strategies

Extending with mobility, name-handling,…

Apply to existing models to make them

parametric w.r.t. synchronization strategies

Studying models where different

synchronization strategies coexist

– SHR good for first analysis