1 Synchronization strategies for global computing models Ivan Lanese Computer Science Department University of Bologna

2 Roadmap Application field: global computing The main tool: graphs and SHR Some contributions –Parametric synchronization –Compositionality properties –Relations with Fusion Calculus And after?

3 What is global computing? Essentially networks deployed on huge areas Global computing systems quite common nowadays –Internet, wireless communication networks,…

4 Challenges of global computing systems Distribution, mobility, heterogeneity, openness, reconfigurability, non-functional requirements Traditional formal methods are not enough –Strong emphasis on coordination among subsystems –Mobility must be modeled explicitly –Need for compositionality and high abstraction

5 Synchronized Hyperedge Replacement We want to model systems as graphs Components are edges Links are common nodes Behaviour specified by transitions –Derived from the behaviour (productions) of single components –Keep into account synchronization and communication/mobility

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

7 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

8 Synchronizing productions Synchronization: productions execute actions on nodes. Actions on the same node should be compatible Two existing synchronization models: Milner (message passing) and Hoare (agreement)

9 Milner SHR Milner synchronization: pair of edges can synchronize by performing complementary actions a A1 a B1 a A2 a B1B2 A2B2

10 SHR with mobility – Actions carry references to nodes – References associated to synchronized actions are matched and corresponding nodes are merged We use node mobility a A1 a A1B1 a A2 a B1B2 A2B2 xy x=y

11 Example x Initial Graph C Brother: C C C C S Star Reconfiguration: w r x C Brother C C C C C C CCC (4)(3)(2)(1) Star Rec. S S SS (5)

12 Algebraic presentation of SHR Helps the development of the theory –Proofs by induction Graphs represented as terms in an algebra –Edges are basic constants –Operators for composing them Transitions described by a labelled transition system Inference rules to derive transitions from productions

13 Parametric synchronization The expressive powers of Hoare and Milner synchronizations are not comparable –Can specify different classes of reconfigurations Is it possible to find some more general framework? Winskel proposed synchronization algebras to describe general synchronizations –Not suitable for synchronizations with mobility We generalize them to SAMs (Synchronization Algebras with Mobility)

14 Synchronization Algebras with Mobility

15 Synchronization Algebras with Mobility SAs specify composition of actions –(a,a, τ ) a synchronizes with a producing τ SAMs also provide –Mapping from parameters of synchronizing actions to parameters of the result –Fusions among parameters –Some more technical stuff

16 Milner SAM on 2 actions in, out, τ, ε l (in, out, τ) l (a, ε, a) aε a inout τ

17 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 for any SAM or for a class of SAMs Many SAMs can be used in the same model –Useful to model heterogeneous systems

18 Compositionality for parametric SHR Bisimulation allows to observe interactions of a system with the environment –Can be defined in a standard way for SHR Bisimulation is a congruence for SHR with most SAMs –Behaviour of a system can be inferred from the behaviour of its components

19 Fusion Calculus Calculi for mobility allow to model concurrent and mobile systems –π-calculus is the most used Fusion Calculus generalizes and simplifies it –More symmetric –Shared-state update

20 Milner SHR vs Fusion Calculus Apparently very different models Some important similarities –Synchronization in Milner style –Mobility using fusions Faithful mapping of Fusion into Milner SHR SHR is more general –Graphical presentation –Multiple synchronizations –Concurrent semantics

21 Fusion Calculus vs Milner SHR FusionMilner SHR ProcessesGraphs Sequential processesHyperedges NamesNodes Comm. primitivesProductions TransitionsInterleaving tr.

22 Example

23 Exploitation of the mapping The results obtained for SHR can be applied to Fusion Calculus PRISMA Calculus = Fusion + SAMs The semantics of Fusion induced by the mapping is compositional –The result does not hold for the standard semantics –The trick is concurrency

24 Future work Some applications to π -calculus –Analysis of the concurrent semantics of π -calculus –Application of SAMs to π -calculus From global computing to service oriented computing –In service oriented computing services are discovered, invoked and composed –Which are the correct primitives to model them? –Which are the interesting properties and equivalences?

25 End of talk