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Deterministic Negotiations : Concurrency for F ree

Deterministic Negotiations : Concurrency for F ree. Javier Esparza Technische Universität München Joint work with Jörg Desel and Philipp Hoffmann. (Multiparty) negotiation. Negotiation as concurrency primitive. Concurrency theory point of view: N egotiation = synchronized choice.

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Deterministic Negotiations : Concurrency for F ree

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  1. DeterministicNegotiations:ConcurrencyforFree Javier Esparza Technische Universität München Joint work with Jörg Deseland Philipp Hoffmann

  2. (Multiparty) negotiation

  3. Negotiation as concurrency primitive • Concurrency theory point of view: Negotiation = synchronized choice • CSP: • Petri nets: a b • Negotiations: a net-like concurrency model with negotiation as primitive.

  4. The Father-Daughter-Mother Negotiation Daughter Agents Initial states Father 11:00 pm Daughter 2:00 am Mother 10:00 pm

  5. The Father-Daughter-Mother Negotiation

  6. The Father-Daughter-Mother Negotiation Atomic negotiations (atoms)

  7. The Father-Daughter-Mother Negotiation Initial atom Final atom

  8. An atomic negotiation Parties: subset of agents Outcomes: yes, no, ask_mum Outcomes: yes, no, ask_mum Outcomes: yes, no, ask_mum State transformers (one per outcome):

  9. Semantics 11:00 2:00 10:00 11:00 2:00 10:00 12:00 12:00 10:00 12:00 12:00 12:00

  10. Semantics 11:00 2:00 10:00 11:00 2:00 10:00 2:00 11:00 10:00 Angry! 11:00 Angry! Beer! Angry! Angry!

  11. Negotiations as Parallel Computation Model.Parallel Bubblesort 3 5 2 7 1 • Four agents. • Internal states: integers. • Transformer of internalbinaryatom: swap integers if not in ascending order.

  12. Negotiations and Petri nets • Negotiations have the same expressive power as (coloured) 1-safe Petri nets, but can be exponentially more succint.

  13. Analysis problems: Soundness Deadlock!

  14. Analysis problems: Soundness • Large step: sequence of occurrences of atoms starting with the initial and ending with the final atom. • A negotiation is sound if • Every execution can be extended to a large step. • No useless atoms: every atom occurs in some large step. (cf. van der Aalst’s workflow nets) • In particular: soundness → deadlock-freedom

  15. Analysis problems: Summarization • Each large step induces a relation between initial and final global states • The summary of a negotiation is the union of these relations (i.e., the whole input-output relation). • The summarization problem consists of, given a sound negotiation, computing its summary.

  16. Computing summaries • A simple algorithm to compute a summary: • Compute the LTS of the negotiation • Applyreduction rules State explosion! Merge Shortcut Iteration

  17. Computing summaries Theorem [CONCUR 13]: deciding if a giving pair of global states belongs to the summary of a given negotiation is PSPACE-complete, even for every simple transformers. Restrictionto: DETERMINISTIC NEGOTIATIONS

  18. Deterministicnegotiations • A negotiation is deterministicifnoagentisever ready to engage in more than oneatom • Graphically: no proper hyperarcs. non-deterministic

  19. Deterministic negotiations • A negotiation is deterministic if no agent is ever ready to engage in more than one atom • Graphically: no proper hyperarcs. deterministic

  20. Det. Negotiations: Reduction Rules • Aim: find reduction rules acting directly on negotiation diagrams (instead of their transition systems). • Rules must: • preserve soundness: sound after iff sound before; and • preserve the summary: summary after equal to summary before • In [CONCUR 13] wepresentthreelocal rules: application conditions and changes involve only a local neighbourhood of the application point.

  21. Rule 1: Merge ,

  22. Rule 2: iteration

  23. Rule 3: shortcut Orange atom enables whiteatomuncondi-tionally.

  24. Completeness and polynomiality • A set of rules is complete for a class if it reduces all negotiations in the class to atomic negotiations. • A complete set of rules is polynomial if every sound negotiation with k atoms is reduced to an atom by rule applications, for some polynomial p.

  25. The Reducibility Theorem • Theorem [CONCUR 13,FOSSACS 14]: • The shortcut, merge, anditerationrulesare completeandpolynomialfordeterministicnegotiations (Also; extensiontoacyclic, weaklydeterministicnegotiations, like theFather-Daughter-Mother neg.) • Concurrencyforfree: • Soundness decidable in polynomial time. • Summarizationascomplexas in thesequentialcase. No additional „exponential“ due tostateexplosion.

  26. Scenarios/Choreographies • Scenario: Concurrentrunofthesystem (usecase) „Global view“ of an execution. Message-passing Message Sequence Chart Source: Harel

  27. Scenario-basedSpecifications • Specification: „regularset“ ofscenarios Message-passing Message Sequence Graph Source: Bille andKosse

  28. Scenario-basedSpecifications • Implementation: communicatingautomata Message-passing Channel systems Source: Schnoebelen

  29. The Realizability Problem • Given a specification, automaticallycompute a realization (implementation), ifthereisone. Message-passing [Alur et al. 01] • Not everyspecificationisrealizable • Realizabilityisundecidable • Deadlock-freerealizability in EXPSPACE and PSPACE-hard

  30. Scenario Mazurkiewicztrace RealizabilityforDeterministicNegotiations We design a programminglanguagefordeterministicnegotiations Implementation Det. Negotiation A B C D Andthespecificationmodel ?

  31. Negotiationprograms • A negotiationprogramisdefinedover: • a setofagents, and • a set of actions • Eachactionisjointlyexecutedby a subset of theagentsof • (cf. distributedalphabets)

  32. Negotiationprograms • A negotiationprogramiseither: • theemptyprogram

  33. Negotiationprograms • A negotiationprogramiseither: • theemptyprogram • a do-od block • do [] end …[] end • [] loop … [] loop • od

  34. A programminglanguage • A negotiationprogramiseither: • theemptyprogram • a do-od block • do [] end …[] end • [] loop … [] loop • od • a layeredcomposition • [Zwiers et al, early 90s]

  35. Mazurkiewicztracesemantics • Weassign a negotiationprogram a setofMazurkiewicztracesovertheprogramactions Agents D B C aa A Actions

  36. Semanticsoflayeredcomposition Semanticsof:traceconcatenation Trace of Trace of Trace of C B A B C A B

  37. Semanticsoflayeredcomposition

  38. Semanticsofblocks Abbreviation: 

  39. An example

  40. An example

  41. Programmingdeterministicnegotiations

  42. Programmingdeterministicnegotiations

  43. Programmingdeterministicnegotiations

  44. Programmingdeterministicnegotiations

  45. Programmingdeterministicnegotiations

  46. The RealizabilityTheorem Theorem (submitted): • Foreverynegotiationprogramofsize thereis a SOUND det.negotiationofsize such that. • ForeverySOUNDdet. negotiationofsizethereis a negotiationprogramofsize such that.

  47. The Realizability Theorem In realizabilityterms: Allspecificationscanbeimplemented, withoutblowup, in linear time. Allspecificationsaresound (and so deadlock/livelock-free). Allsoundimplementations canbespecified.

  48. Fromnegotiationstoprograms • We useourcompletesetofreductionrulesforsounddeterministicnegotiations (SDNs). • Forevery SDN thereis a sequence of negotiationssuch that • , • isobtainedfrombyapplying a rule, and • isthenegotiationoftheemptyprogram

  49. Fromnegotiationstoprograms • For thereversesequence obtainedbyaplyingthereverseofthereductionrules (synthesisrules), weconstruct a matchingsequenceofprograms such thatforevery

  50. Fromnegotiationstoprograms Shortcut rule, case 2

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