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On the Formalization and Comparison of Coordination Models and Languages

On the Formalization and Comparison of Coordination Models and Languages. Gianluigi Zavattaro. Department of Computer Science University of Bologna. Plan of the Talk. Coordination Infrastructures Data- vs Event-driven coord. (informally) Shared Dataspaces (formally)

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On the Formalization and Comparison of Coordination Models and Languages

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  1. On the Formalization and Comparison of Coordination Models and Languages Gianluigi Zavattaro Department of Computer ScienceUniversity of Bologna

  2. Plan of the Talk • Coordination Infrastructures • Data- vs Event-driven coord. (informally) • Shared Dataspaces (formally) • Publish/Subscribe (formally) • Dataspace  Pub/Sub • Pub/Sub  Dataspace + Global Op. Validation02 - Genova - 22/11/2002

  3. A Data-driven Coordination Infrastructure TSpaces Coordination Infrastructures: a Classification • An Event-driven Coordination Infrastructure Talarian SmartSockets Validation02 - Genova - 22/11/2002

  4. Common Features • No direct Communication • Communication mediated by the infrastructure • Space Uncoupled Communication • No channel topology • Time Uncoupled Communication • Asynchronous communication • Associative Communication • Communication based on content or subject Validation02 - Genova - 22/11/2002

  5. Motivation • How much critical is the choice of the kind of infrastructure in the design of a coordinated system? • Are event- and data-driven infrastructures interchangeable? • Can each event-driven system be reduced to an equivalent data-driven system without altering the internal behavior of the processes, and vice versa? Validation02 - Genova - 22/11/2002

  6. Plan of the Talk • Coordination Infrastructures • Data- vs Event-driven coord. (informally) • Shared Dataspaces (formally) • Publish/Subscribe (formally) • Dataspace  Pub/Sub • Pub/Sub  Dataspace + Global Op. Validation02 - Genova - 22/11/2002

  7. The Units of Coordination • Event-driven coordination • Processes raise events • An event is delivered to the processes which subscribed their interest to its specific type • Data-driven coordination • Processes produce data • A datum may be accessed (read or consumed) from all process in the system Validation02 - Genova - 22/11/2002

  8. The production of the Units of Coordination is Non-Blocking Creation • An event can be raised whatever is the current state of the system • A datum can be produced whatever is the current content of the shared repository Validation02 - Genova - 22/11/2002

  9. Lifetime • An event plays a role in the system until its multicast finishes • Implicitly received/removed from the system • A datum remains in the shared repository until it is explicitly withdrawn • Explicitly read/consumed Validation02 - Genova - 22/11/2002

  10. Visibility • An event is visible only and exactly to the subscribed processes • Restricted visibility • A datum can be read/consumed by each process in the system • Global visibility Validation02 - Genova - 22/11/2002

  11. Plan of the Talk • Coordination Infrastructures • Data- vs Event-driven coord. (informally) • Shared Dataspaces (formally) • Publish/Subscribe (formally) • Dataspace  Pub/Sub • Pub/Sub  Dataspace + Global Op. Validation02 - Genova - 22/11/2002

  12. A Shared DataspaceProcess Calculus (DS) C ::= 0 | <a> | P | C|C P::= out(a).P | in(a).P | rd(a).P | eval(P).P | K • With a taken from Names and constant definition K=P Validation02 - Genova - 22/11/2002

  13. <c> T DS semanticsGraphically out(c).P rd(b).Q <b> <a> <b> in(a).R eval(T).S Validation02 - Genova - 22/11/2002

  14. DS semanticsReduction relation (some rules) out(a).P  <a> | P in(a).P | <a>  P rd(a).P | <a>  P | <a> eval(P).Q  P | Q • Assuming commutativity and associativity of parallel comp. Validation02 - Genova - 22/11/2002

  15. Plan of the Talk • Coordination Infrastructures • Data- vs Event-driven coord. (informally) • Shared Dataspaces (formally) • Publish/Subscribe (formally) • Dataspace  Pub/Sub • Pub/Sub  Dataspace + Global Op. Validation02 - Genova - 22/11/2002

  16. A Publish/Subscribe Process Calculus (PS) C ::= 0 | on(e,P) | P | C|C P::= pub(e).P | sub(e,P).P |unsub(e,P).P | new(P).P | K • With e taken from Events and constant definition K=P Validation02 - Genova - 22/11/2002

  17. P on(e,P) on(f,S) on(e,Z) Z U PS semanticsGraphically sub(e,P).Q unsub(f,S).T pub(e).R new(U).V Validation02 - Genova - 22/11/2002

  18. PS semanticsLabeled Transition Syst. (some rules) sub(e,P).Q  on(e,P) | Q unsub(e,P).Q | on(e,P)  Q on(e,P) e on(e,P) | P pub(e).P e P P e P’ Q e Q’ P | Q e P’ | Q’ Validation02 - Genova - 22/11/2002

  19. Plan of the Talk • Coordination Infrastructures • Data- vs Event-driven coord. (informally) • Shared Dataspaces (formally) • Publish/Subscribe (formally) • Dataspace  Pub/Sub • Pub/Sub  Dataspace + Global Op. Validation02 - Genova - 22/11/2002

  20. Reducing DS into PS • Mapping entities of Dataspaces into entities in Pub/Sub • Data = listeners • Output = listener production • Input = listener consumption • Read = Input+Output Validation02 - Genova - 22/11/2002

  21. The Reduction Function [[ 0 ]] = 0 [[ K ]] = K (with K = [[ P ]]) [[ out(a).P ]] = sub(ea,0).[[ P ]] [[ in(a).P ]] = unsub(ea,0).[[ P ]] [[ rd(a).P ]] = unsub(ea,0).sub(ea,0).[[ P ]] [[ eval(P).Q ]] = new([[ P ]]).[[ Q ]] Validation02 - Genova - 22/11/2002

  22. Plan of the Talk • Coordination Infrastructures • Data- vs Event-driven coord. (informally) • Shared Dataspaces (formally) • Publish/Subscribe (formally) • Dataspace  Pub/Sub • Pub/Sub  Dataspace + Global Op. Validation02 - Genova - 22/11/2002

  23. Impossibility of any satisfactory reduction No Reduction of DS into PS • A satisfactory reduction should preserve at least termination • [[ C ]] may terminate iff C may terminate • The existence of a terminating computation is • Decidable in DS (reduction of DS to finite P/T nets) • Undecidable in PS (reduction of RAMs into PS) Validation02 - Genova - 22/11/2002

  24. Reducing PS into finite P/T nets out(a).P in(a).Q <a> P Q Validation02 - Genova - 22/11/2002

  25. Random Access Machine (RAM) • Registers: r1 … rn hold natural numbers • Program: sequence of numbered instructions • Inc(rj): add 1 to the content of rj and go to the next instruction • DecJump(rj,s): if the content of rjis not 0 then decrease by 1 and go to the next instruction; otherwise jump to instruction s Validation02 - Genova - 22/11/2002

  26. Registers Instructions on(r1,pub(r1)) … on(i1,[[ins1]]) … on(r1,pub(r1)) on(in,[[insn]]) on(rm,pub(rm)) … on(rm,pub(rm)) Encoding RAM in PS(the idea) DecJump(rj,s): Non-det. choice between Decrement = loop until decrement succeeds Jump = publish rj and jump to instruction s Validation02 - Genova - 22/11/2002

  27. Properties of the RAM encoding • Only termination is preserved: RAM  iff [[ RAM ]] Oss: By C we mean the existence of a completed finite computation • Can we define also a divergence preserving encoding?Answer: no because the existence of an infinite computation is decidable Validation02 - Genova - 22/11/2002

  28. Decidability of Divergence • We express PS in terms of P/T nets with transfer arcs (divergence is decidable [DFS98]) sub(e,P).Q pub(e).R on(e,P) Q start(P,a) R Validation02 - Genova - 22/11/2002 P

  29. P P Adding Global Operation • We extend DS with a global operation (inspired by copy-collect) ccollect(a,P).Q <a> <c> <a> <b> Validation02 - Genova - 22/11/2002

  30. Reducing PS into DS • Listeners = data • on(e,P) = lsteP • Subscribe = data production • [[ sub(e,P) ]] = out(lsteP) • Unsubscribe = data consumption • [[ unsub(e,P) ]] = in(lsteP) • Publish = count each kind of listeners • [[ pub(e) ]] = ccollect(lsteP1,P1)…ccollect(lstePn,Pn) Validation02 - Genova - 22/11/2002

  31. Conclusion Termination Undecidable Divergence Decidable + Glob. Operators PS calculus DS calculus Termination Decidable Validation02 - Genova - 22/11/2002

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