Synchronization strategies for global computing models

1
Synchronization strategiesfor global computing
models
Ivan Lanese Computer Science Department University
of Bologna
2
Roadmap

• Global computing
• Synchronized Hyperedge Replacement
• SHR vs Fusion Calculus
• Synchronization Algebras with Mobility
• Congruence results
• Future work

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Roadmap

• Global computing
• Synchronized Hyperedge Replacement
• SHR vs Fusion Calculus
• Synchronization Algebras with Mobility
• Congruence results
• Future work

4
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
• Synchronized Hyperedge Replacement
• SHR vs Fusion Calculus
• Synchronization Algebras with Mobility
• Congruence results
• Future work

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Synchronized Hyperedge Replacement

• 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

L
R
H
3
3
4
4
2
2
1
1
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Hyperedge Replacement Systems

• A production describes how the hyperedge L is
  transformed into the graph R

Many concurrent rewritings are allowed
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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

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SHR with mobility
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Example
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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
• Synchronized Hyperedge Replacement
• SHR vs Fusion Calculus
• Synchronization Algebras with Mobility
• Congruence results
• Future work

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Fusion Calculus

• Calculus for mobility inspired by p-calculus
• Input prefix is not a binder
• Symmetric input/output
• Names are merged
• Input of p-calculus obtained as inputrestriction
  on the objects of the input

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SHR vs Fusion Calculus

• 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
We can also execute both the steps at the same
time
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Roadmap

• Global computing
• Synchronized Hyperedge Replacement
• SHR vs Fusion Calculus
• Synchronization Algebras with Mobility
• Congruence results
• Future work

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Synchronization Algebras with Mobility (1)

• Extend Winskels 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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Synchronization Algebras with Mobility (2)
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Synchronization Algebras with Mobility (2)

• SAs specify composition of actions
• (a,a,t) a synchronizes with a producing t
• 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, t, e
• e stands for not taking part to the
  synchronization
• Normal actions synchronize with corresponding
  coactions giving t, corresponding parameters are
  fused, no parameters are propagated
• Anything can synchronize with e, action and
  parameters are propagated, no fusions
• No other synchronization is allowed
• Only t and e 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
• Synchronized Hyperedge Replacement
• SHR vs Fusion Calculus
• Synchronization Algebras with Mobility
• Congruence results
• Future work

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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

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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 p-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 ab can execute a and b concurrently
  going to 0 (but can also execute either a or b)
• Process aa is bisimilar to a.a
• Process aab can perform t 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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Congruence properties

• no more a
  counterexample since the two terms are not
  bisimilar

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Congruence properties

• 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 at in addition to normal t
• The resulting bisimilarity is a congruence

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Roadmap

• Global computing
• Synchronized Hyperedge Replacement
• SHR vs Fusion Calculus
• Synchronization Algebras with Mobility
• Congruence results
• Future work

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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
  p-calculus
• Applying SAMs to p-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. Hirsch and U. Montanari,
  Proceedings of CONCUR 2001, LNCS 2154
• 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-VC05, 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

• Thanks

• Questions?