Synchronization strategies for global computing

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• PRISMA

A mobile calculus with parametric synchronization
Ivan Lanese Computer Science Department University
of Bologna Roberto Bruni Computer Science
Department University of Pisa
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Roadmap

• Why PRISMA calculus?
• Synchronization Algebras with Mobility
• Syntax and semantics
• Properties and applications
• Conclusions and future work

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Roadmap

• Why PRISMA calculus?
• Synchronization Algebras with Mobility
• Syntax and semantics
• Properties and applications
• Conclusions and future work

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Process calculi and synchronization

• Process calculi are used to model a wide range of
  systems
• Computer networks, biological systems, service
  oriented architectures, workflow patterns
• Different systems communicate according to
  different synchronization policies
• Each calculus has its own primitive(s)
• Binary synchronization, broadcast, service
  invocation

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Modelling troubles

• Sometimes the desired primitives are not (all)
  available in the used calculus
• Either they should be implemented
• Difficult task, produces unclear models
• or a new ad hoc model is proposed
• Theory and tools have to be redeveloped from
  scratch

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Our idea

• Define a (mobile) calculus where the
  synchronization primitives can be freely chosen,
  combined and compared
• We build on
• Winskels work on synchronization algebras
• Do not consider mobility
• Our previous work on synchronization algebras
  with mobility in the Synchronized Hyperedge
  Replacement framework
• Belongs to the graph transformation approach
• We apply the idea in the field of calculi for
  mobility

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What we are claiming and NOT claiming

• Our calculus is NOT able to easily and faithfully
  simulate each possible calculus
• Synchronization is not the only feature that
  characterize a calculus
• But
• Real systems can be more easily modelled since
  the desired primitives can be defined and
  exploited
• Shows how to use the parametric approach for
  mobile calculi
• Is a first step towards the understanding of the
  commonalities / differences between different
  calculi

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A sample scenario

• A news server takes news from providers and
  broadcasts them to clients
• Two kinds of primitives
• Binary communication between providers and the
  server
• Broadcast between server and clients
• Challenging scenario for previous calculi (e.g.,
  p calculus)

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Roadmap

• Why PRISMA calculus?
• Synchronization Algebras with Mobility
• Syntax and semantics
• Properties and applications
• Conclusions and future work

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Synchronization Algebras with Mobility

• Abstract formalization of a synchronization
  policy
• A SAM contains
• A set of ranked actions Act
• An element e standing for not taking part to the
  synchronization
• A set of action synchronizations of the form (a,
  b, (c, Mob, ?))
• Actions a and b can interact, producing action c
• The parameters of a and b are merged according to
  ?
• The parameters of c are computed as described by
  Mob
• A subset Fin of Act containing the complete
  actions
• Allowed on restricted channels
• SAMs must satisfy some coherence conditions

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Mob and ?
a
b
c
Mob
?
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Milner synchronization as a SAM

• Actions inputs (e.g., in), outputs (e.g., out),
  t, e
• No other synchronization is allowed
• Only t and e are in Fin

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Broadcast synchronization as a SAM

• Actions inputs, outputs, e
• e can synchronize only with itself
• Only out and e are in Fin
• As a result a complete synchronization involves
  one out and one in from each other partner

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Roadmap

• Why PRISMA calculus?
• Synchronization Algebras with Mobility
• Syntax and semantics
• Properties and applications
• Conclusions and future work

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PRISMA Calculus syntax

• Standard process calculi operators
• Parallel composition, restriction, choice,
• Prefixes x a y allowing to perform action a on
  channel x with parameters in y

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PRISMA Calculus syntax

• Standard process calculi operators
• Parallel composition, restriction, choice,
• Prefixes x a y allowing to perform action a on
  channel x with parameters in y
• Example

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PRISMA semantics

• Given by an LTS
• Reduction semantics not suitable for multi-party
  synchronization
• The behavior of a PRISMA process depends on the
  chosen SAM S
• Inference rules parametric on S to derive
  labelled transitions
• label (Y) x a y, p executes x a y extruding names
  in Y and applying fusion p
• label v, p executes an action on a restricted
  channel applying fusion p

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Implementing the news scenario

• News server
• Provider
• Clients

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Abstract semantics

• Bisimilarity can be defined in a standard way
• Basic axioms (e.g., commutativity and
  associativity of parallel composition) bisimulate
  for any SAM
• Theorem
• Hyperbisimilarity (substitution closed
  bisimilarity) is a congruence for any SAM

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Roadmap

• Why PRISMA calculus?
• Synchronization Algebras with Mobility
• Syntax and semantics
• Properties and applications
• Conclusions and future work

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PRISMA vs Fusion

• Fusion calculus can be easily translated into
  Milner PRISMA
• Homomorphic extension of the translation of
  Fusion inputs and outputs into PRISMA ones
• The obtained semantics is more detailed than
  standard Fusion one
• Shows on which (free) channel a fusion is
  generated
• The induced bisimilarity is more detailed too

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Composing SAMs

• SAMs can be given a categorical structure
• Categorical constructions allow to combine SAMs
• Coproduct makes the union of the primitives
• Product creates compound primitives
• The SAM used in the sample application is a
  coproduct of a Milner SAM and a broadcast SAM

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Translating processes

• A process on S1 can be translated along a
  morphism HS1?S2 to a process on S2
• Allows to execute a process in a different
  framework
• Properties of the morphism ensure preservation of
  part of the behaviour
• Translations along isomorphisms preserve
  bisimilarity

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A sample application

• Priority SAM many outputs synchronize with one
  input, the one with the highest priority is
  received
• Suppose we want to execute a Fusion process PF in
  this framework
• We can translate it into a Milner PRISMA process
  PM
• There is a morphism Hn from Milner to Priority
  assigning priority n to each output
• Hn(PM) is a priority process

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Roadmap

• Why PRISMA calculus?
• Synchronization Algebras with Mobility
• Syntax and semantics
• Properties and applications
• Conclusions and future work

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Conclusions

• PRISMA is a mobile calculus suitable to model
  different kinds of systems
• Heterogeneous systems
• Suitable for interoperability analysis
• Allows to reuse theory and tools for different
  applications

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Future work

• Put PRISMA at work on more challenging case
  studies
• Exploit PRISMA to compare different
  synchronization models
• Analyze the relationships with existing calculi

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End of talk

• Thanks

• Questions?