1 Ivan Lanese Computer Science Department University of Pisa Prof. Ugo Montanari Synchronization strategies for global computing Relator: Thesis Progress Report

2 Roadmap Global computing SHR and other formal tools What we did in the first year What we planned after the first year What we have done What is still to be done

3 Roadmap Global computing SHR and other formal tools What we did in the first year What we planned after the first year What we have done What is still to be done

4 What is global computing? Essentially networks deployed on huge areas It is becoming the most widespread computing paradigm –Internet, wireless communication networks, overlay networks …

5 Features of global computing systems Distribution –Huge areas: localities can not always be hidden Mobility –Both physical and code mobility Eterogeneity –Interoperability, coordination Openness Reconfigurability

6 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

7 High level models We look for models at high level of abstraction –Models of coordination among subsystems –For making the model of the whole system treatable We need powerful primitives –Multiple synchronizations –Abstractions of full protocols –Declarative specification of constraints –Possible evolutions derived as solution of system of constraints

8 Roadmap Global computing SHR and other formal tools What we did in the first year What we planned after the first year What we have done What is still to be done

9 Synchronized Hyperedge Replacement Follows the traditional approach of graph transformation –Deals well 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 –Global constraint solving algorithm to find allowed transitions –Productions applied indipendently –Allows to define complex transformations –Allows multiple synchronization –Declarative approach

10 Hyperedge Replacement Systems A production describes how the hyperedge L is rewritten into the graph R R L H

11 Hyperedge Replacement Systems A production describes how the hyperedge L is transformed into the graph R R R’ Many concurrent rewritings are allowed L L’ H

12 Synchronizing productions Synchronized transitions: we associate actions to nodes. A transition is allowed iff the synchronization constraints imposed on actions are satisfied Many synchronization models are possible (Hoare, Milner,...)

13 An example: Milner SHR Milner synchronization: pair of edges can synchronize by doing complementary actions a 3 3 B1A1 B2A2 a a a

14 SHR with mobility – Actions carry tuples of references to nodes (new or already existent) – References associated to synchronized actions are matched and corresponding nodes are merged We use name mobility a B1A1 B2A2 a (x)(y) x=y

15 Other formal tools: CommUnity in one slide Architectural model of concurrent systems Based on communication via channels and synchronization of actions Separation between computation and coordination concerns –Computation inside programs –Coordination explicitly represented via morphisms and special programs (cables) –Composition via colimits

16 Other formal tools: Tile Model in one slide Extension of SOS systems and rewriting logic that allows synchronization –Rules have trigger and effect Operators of horizontal, vertical and monoidal composition Useful for studying observational properties of open systems

17 Roadmap Global computing SHR and other formal tools What we did in the first year What we planned after the first year What we have done What is still to be done old

18 Comparing models for GC Comparing synchronization strategies, mobility strategies and binding operators in different models Comparative analysis of the following paradigms –Fusion Calculus: calculus for mobility, allows fusions –SHR: already presented in detail –Logic programming: developed programming paradigm, we use it as goal rewriting mechanism, to be extended to deal with GC systems Mapping of Fusion Calculus into SHR and of SHR into logic programming –Fusion Calculus is a subset of Milner SHR –Logic programming (with transactions) related to Hoare SHR old

19 Comparing strategies for compositionality Two approaches to compositionality –Categorical approach: via universal constructions (colimits) –Algebraic approach: via operators for building systems Our case study: CommUnity vs Tile Model old

20 Results from CommUnity vs tiles Semantics for CommUnity Decomposition of CommUnity programs New algebra of connectors (in the Tile Model) that simulates CommUnity synchronization Correlation between colimit and algebraic aspects (bisimulation, axiomatization) old

21 Roadmap Global computing SHR and other formal tools What we did in the first year What we planned after the first year What we have done What is still to be done plan

22 A physical analogy Physical systems –Many interacting components –Partial derivative equations for parts of the space –Components of the system gives boundary conditions –The solutions of the system of equations are the allowed behaviors Global computing systems –Equations associated to the interfaces –Equations are a declarative way of specifying coordination –Only simple equations used in past works »Hoare and Milner synchronization in SHR Developing new models using this analogy plan

23 Different items Extending synchronization algebras with mobility –Standard synchronization algebras allow to categorize synchronization models –Need extensions to be applied to GC models –SHR well-suited for these analysis Analyzing observational semantics of GC models –Allows to analyze incomplete systems (compositionality) –Tile Logic well-suited for such analysis Hybrid models –For taking the best features of different models –Suggested by the comparisons done plan

24 General aim Double aim: –Analyzing existing models and their relationships –Looking for new models for GC systems plan

25 Roadmap Global computing SHR and other formal tools What we did in the first year What we planned after the first year What we have done What is still to be done ok

26 SAMs (1) Synchronization algebras with mobility –Extend synchronization algebras to deal with name mobility and local resources –Different synchronization policies allowed »Simple ones: Milner, Hoare, broadcast »More complex ones: with priority, treshold synchronization –Like differential equations for physics ok

27 SAMs (2) SAs specify composition of actions SAMs also gives: –Mapping from parameters of synchronizing actions and parameters of the result –Fusions among parameters –Final actions (performed on local channels) –Some more technical stuff ok

28 An example: SAM for Milner synchronization Actions: normal actions, coactions, tau, epsilon Normal actions synchronize with corresponding coactions giving tau, corresponding parameters are fused, no parameters are propagated Anything synchronize with epsilon, action and parameters are propagated, no fusions No other synchronization is allowed Only tau and epsilon can be done on local channels ok

29 Applying SAMs Applied in the context of SHR Parametric SHR –The SAM is a parameter of the model –Different models obtained via instantiation –Properties can be proved in general Heterogeneous SHR –Each node is labelled by a SAM –SAMs are required to form a commutative monoid –Node fusions cause SAMs composition Broadcast fusion calculus –Via the mapping discovered in the first year ok

30 Abstract semantics for SHR Bisimulation for (parametric) SHR Congruence results w.r.t. a suitable algebra of graphs Found using the Tile Model as framework, but then provable indipendently ok

31 Extending CommUnity vs Tile Model (1) Analysis of the class of connectors for CommUnity –3 different semantics for connectors »observational »axiomatic »denotational –The 3 semantics are equivalent –Study of the expressivity of different classes of connectors –The larger class allows to produce a connector for each denotation ∆01 00tickuntick 01untick 10untick 11unticktick ok

32 Extending CommUnity vs Tile Model (2) Double correspondance between categorical and algebraic approach –Starting diagram and colimit equals up to bisimulation –Axiomatization of bisimulation and reduction to normal form allow to compute colimit algebraically ok

33 Roadmap Global computing SHR and other formal tools What we did in the first year What we planned after the first year What we have done What is still to be done todo

34 From planned work More refined abstract semantics –Abstract semantics for SHR is very (too) distinguishing Hybrid models –Models with different synchronization policies have been derived but their properties have to be analyzed in more depth –What about other hybrid models? SAMs –SAMs have been applied to SHR –Can them be applied to other formalisms (process-calculi)? todo

35 New ideas Refining –To bridge the gap between high level models and implementation –Must preserve behavioral properties Combining SHR and bigraphs –Bigraphs and SHR have the same field of application but different aim (double structure vs compositionality) todo

36 Bibliography (old) “Software Architecture, Global Computing and Graph Transformation via Horn Clauses”, I. Lanese and U. Montanari, Proceedings 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, under review for publication in a special issue of TPLP

37 Bibliography (new) “Synchronization algebras with mobility for graph transformations”, I. Lanese and U. Montanari, Proceedings FGUC 2004, ENTCS, to appear “Synchronized Hyperedge Replacement for heterogeneus systems”, I. Lanese and E. Tuosto, submitted to COORDINATION 2005 “New insights on architectural connectors”, R. Bruni, J.L. Fiadeiro, I. Lanese, A. Lopes and U. Montanari, Proceedings IFIP TCS 2004, Kluwer Academics “Normal forms for stateless connectors”, R. Bruni, I. Lanese and U. Montanari, submitted to CALCO 2005

38 End of talk

39 Observational and abstract semantics Analyzing observational and abstract semantics of models –Useful for abstracting details –Important to analyze relationships with compositionality Tile Model is well suited for this kind of analysis –Existing criteria for compositionality too restrictive for GC applications

40 Hybrid models Plugging features from a model into another one Expressiveness and properties of new models must be analyzed Ongoing work: –Logic programming with restriction –Concurrent Fusion Calculus New ideas: –Non Milner Fusion Calculus –Non Hoare logic programming

41 Algebra of synchronization strategies Synchronization algebras –Categorize synchronization strategies Extending with mobility, name-handling,… Apply to existing models to make them parametric w.r.t. synchronization strategies Studying models where different synchronization strategies coexist –SHR good for first analysis