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Ivan Lanese Computer Science Department Univers ity of Bologna Roberto Bruni

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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

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

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

- 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

- 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

- Define a (mobile) calculus where the synchronization primitives can be freely chosen, combined and compared
- We build on
- Winskel’s 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

- Winskel’s work on synchronization algebras
- We apply the idea in the field of calculi for mobility

- Our calculus is NOT able to easily and faithfully simulate each possible calculus
- Synchronization is not the only feature that characterize a calculus
But

- Synchronization is not the only feature that characterize a calculus
- 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

- 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., π calculus)

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

- Abstract formalization of a synchronization policy
- A SAM contains
- A set of ranked actions Act
- An element ε 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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- Actions: inputs (e.g., in), outputs (e.g., out), τ, ε
- No other synchronization is allowed
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- Actions: inputs, outputs, ε
- ε can synchronize only with itself
- Only out and ε are in Fin
- As a result a complete synchronization involves one out and one in from each other partner

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

- 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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- Parallel composition, restriction, choice, …
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- Example:

- 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, πexecutes x a y extruding names in Y and applying fusion π
- label √, π executes an action on a restricted channel applying fusion π

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- 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

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

- 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

- 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

- A process on S1 can be translated along a morphism H:S1→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

- 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

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

- 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

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

Thanks

Questions?