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  1. Ph.D. thesis discussion Synchronization strategiesfor global computing models Ivan Lanese Computer Science Department University of Pisa (moved to Bologna) Supervisor: prof. Ugo Montanari

  2. Roadmap • Global computing • Comparing models for GC • Parametric synchronizations with mobility • Observational semantics and compositionality • Conclusions

  3. Roadmap • Global computing • Comparing models for GC • Parametric synchronizations with mobility • Observational semantics and compositionality • 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

  6. 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

  7. 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

  8. Roadmap • Global computing • Comparing models for GC • Parametric synchronizations with mobility • Observational semantics and compositionality • Conclusions

  9. 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

  10. 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

  11. 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

  12. NOOO!!! Long background on SHR

  13. 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

  14. 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

  15. 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

  16. Summary of the comparison Hoare SHR SLP Graph Goal Hyperedge Atom Node Variable Parallel comp. AND comp. Action Function sym. Production Clause Transition Transaction

  17. An example y y C(x,y)←C(x,z),C(z,y) C C x z C x r<w> y y C(r(x,w),r(y,w))←S(y,w) C S w x x r<w>

  18. C C C x C S C C C C C C Dynamics S S S

  19. C C C x C S C C C C C C Dynamics S S S

  20. Main results • Simple (homomorphic) mapping • Complete correspondance • Suggests how to introduce restriction in logic programming • What about Milner logic programming?

  21. 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

  22. 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.

  23. Example We can also execute both the steps at the same time

  24. Main results • Simple (homomorphic) mapping • Complete correspondance • Suggests many generalizations of Fusion • A concurrent semantics • PRISMA Calculus

  25. 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

  26. 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

  27. 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

  28. Roadmap • Global computing • Comparing models for GC • Parametric synchronizations with mobility • Observational semantics and compositionality • Conclusions

  29. 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

  30. Synchronization Algebras with Mobility (2)

  31. Synchronization Algebras with Mobility (2) • 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

  32. Sample synchronization a b c

  33. τ in out a a ε Milner SAM • Normal actions, coactions, τ, ε • (in, out, τ) • (a, ε, a) • Final actions: τ, ε

  34. 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

  35. 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

  36. 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

  37. inBo Take-off transition univ univ chk inPl inBo chk inPl

  38. at in newat at chk in Specifying the transition (1) at:<ε,<>> in:<ack,<at>> at:<req,<newat>> chk: <breq,<in>> in:<ε,<>>

  39. newat chk at Specifying the transition (2) at:<ε,<>> chk: <brd,<newat>>

  40. Synchronization in the example ε,<> Can be obtained using as SAM the coproduct of: • Milner SAM for req and ack • Broadcast SAM for breq and brd univ ack,<univ> inBo ε,<> ε,<> req,<newat> ε,<> brd,<new1> breq,<inPl> chk ε,<> brd,<new2> inPl

  41. Effects of the synchronization ε univ inBo τ univ/newat breq,<inPl> chk ε inPl/new1,inPl/new2 inPl

  42. Result of the transition univ chk inBo inPl

  43. 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

  44. 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

  45. 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

  46. comm,16,× Building a virtual channel R C Act 4,√ R 16,× 16,√ 4,× 16,√ 4,√ Act C 16,× R R

  47. 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

  48. 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

  49. 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

  50. Roadmap • Global computing • Comparing models for GC • Parametric synchronizations with mobility • Observational semantics and compositionality • Conclusions