1 Ivan Lanese Computer Science Department University of Pisa (moved to Bologna) Synchronization strategies for global computing models Ph.D. thesis discussion 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 → 2 N 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 Long background on SHR NOOO!!!

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 SHRSLP GraphGoal HyperedgeAtom NodeVariable Parallel comp.AND comp. ActionFunction sym. ProductionClause TransitionTransaction

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

18 Dynamics x C C C C C C C CCC S S S S

19 Dynamics x C C C C C C C CCC S 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 FusionMilner SHR ProcessesGraphs Sequential processesHyperedges NamesNodesParallel comp. ScopeRestriction PrefixesProductions TransitionsInterleaving 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 abc

33 Milner SAM Normal actions, coactions, τ, ε l (in, out, τ) l (a, ε, a) l Final actions: τ, ε aε a inout τ

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 Take-off transition univ inBo chk inPl

38 Specifying the transition (1) at: > in: > chk: > newat in chk at at: > in: > at in

39 Specifying the transition (2) at: > chk: > newat chkat

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

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

42 Result of the transition univ inBo inPl chk

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 l Network with routers and clients l Channels can have –4Kb/16Kb packets –Error detection/no error detection l To communicate a client creates a virtual communication channel that uses the underlying infrastructure l The communication channel supports 16Kb packets/error detection only if all the underlying channels do

45 Modeling the scenario l Eight different SAMs with all the combinations of –4Kb < 16Kb –No error detection < error detection –Communication < control l SAMs provide variants of Milner synchronization –E.g. action for detecting errors l SAMs form a partial order (pointwise) l SAM composition corresponds to glb

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

47 Ideas on the derivation l Each production poses some constraints on the features of the resulting channel l During synchronization the constraints are composed according to the specified pattern l 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

51 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 Proof exploits bialgebraic techniques

52 Congruence results for Fusion Calculus Bisimilarity is not a congruence for Fusion Calculus (not closed under substitutions) The comparison with SHR shows why it fails and suggests how to solve the problem We have proposed a new concurrent semantics

53 The idea of the semantics

54 The idea of the semantics Allowing many actions in the same transition but on different channels –Process a|b can execute a and b concurrently going to 0 (but can also execute either a or b) –Process a|a is bisimilar to a.a –Process a|a|b can perform τ and b concurrently going to 0 Allows to observe the degree of parallelism of a process

55 Congruence properties

56 Congruence properties no more a counterexample since the two terms are not bisimilar

57 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 a τ in addition to normal τ The resulting bisimilarity is a congruence

58 Observational semantics of PRISMA Hyperbisimilarity is a congruence Common axioms bisimulate for each SAM A translation along a morphism can be used to change the used SAM Translations along isomorphisms preserve bisimilarity

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

60 Conclusions on SHR SHR is an interesting model for GC –Deals well with distribution, synchronization, mobility –Can be extended to deal with eterogeneity –Good compositionality features have been proved –Some extensions for dealing with non-functional requirements are under analysis [Hirsch & Tuosto] Strong connections with process calculi –Allow cross-fertilization

61 Conclusions on synchronization models Synchronization and mobility patterns are a dimension in the space of GC models –Can be factored out l Parametric models help modeling phase l Different SAMs can –be composed –interoperate

62 Conclusions on compositionality l General and original result on compositionality for graph transformations l Interesting result for Fusion Calculus –Connection between concurrency and compositionality

63 Future work l Further analysis required in many directions l Exploiting the mappings for cross-fertilization l Comparing SHR with other graph transformation frameworks l Analyzing the properties of the new models l Moving from Fusion towards π-calculus l Techniques for proving compositionality

64 Future work l Further analysis required in many directions l Exploiting the mappings for cross-fertilization –Milner logic programming –Multiple synchronizations in process calculi l Comparing SHR with other graph transformation frameworks l Analyzing the properties of the new models l Moving from Fusion towards π-calculus l Techniques for proving compositionality

65 Future work l Further analysis required in many directions l Exploiting the mappings for cross-fertilization l Comparing SHR with other graph transformation frameworks –DPO –Bigraphs l Analyzing the properties of the new models l Moving from Fusion towards π-calculus l Techniques for proving compositionality

66 Future work l Further analysis required in many directions l Exploiting the mappings for cross-fertilization l Comparing SHR with other graph transformation frameworks l Analyzing the properties of the new models –Concurrent Fusion –PRISMA Calculus l Moving from Fusion towards π-calculus l Techniques for proving compositionality

67 Future work l Further analysis required in many directions l Exploiting the mappings for cross-fertilization l Comparing SHR with other graph transformation frameworks l Analyzing the properties of the new models l Moving from Fusion towards π-calculus –Concurrent π-calculus –Parametric π-calculus l Techniques for proving compositionality

68 Future work l Further analysis required in many directions l Exploiting the mappings for cross-fertilization l Comparing SHR with other graph transformation frameworks l Analyzing the properties of the new models l Moving from Fusion towards π-calculus l Techniques for proving compositionality –Bialgebraic techniques requires complex semantics

69 Bibliography of the thesis “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, TPLP, special issue, to appear “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 “Insights Emerged while Comparing Three Models for Global Computing”, I. Lanese and U. Montanari, Proceedings of Dagstuhl seminar on Foundations of Global Computing, Electronic proceedings, 2005 “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-VC‘05, ENTCS, to appear

70 Other publications “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 “On Graph(ic) Encodings”, R. Bruni and I. Lanese, Proceedings of Dagstuhl seminar on Graph transformations and process algebras for modeling distributed and mobile systems, Electronic proceedings, 2004 “New Insights on Architectural Connectors”, R. Bruni, J. Fiadeiro, I. Lanese, A. Lopes and U. Montanari, Proceedings of IFIP TCS’04, Kluwer “Complete Axioms for Stateless Connectors”, R. Bruni, I. Lanese and U. Montanari, Proceedings of CALCO’05, LNCS 3629 “A Basic Algebra of Stateless Connectors”, R. Bruni, I. Lanese and U. Montanari, TCS, to appear "Exploiting User-Definable Synchronizations in Graph Transformation", I. Lanese, Proceedings of GT-VMT'06, ENTCS, to appear

71 End of talk