Modelling MAC-Layer Communications in WirelessSystems(Extended Abstract)Andrea Cerone 1,Matthew Hennessy 1 and Massimo Mer...
OverviewCalculus of Collision-proneCommunicating Processes (CCCP)Contextual EquivalenceCoinductive Characterisation(A. Cer...
OverviewCalculus of Collision-proneCommunicating Processes (CCCP)Modelling Networks at the MAC-sublayer ofthe ISO/OSI refe...
OverviewCalculus of Collision-proneCommunicating Processes (CCCP)Contextual EquivalenceInterchange two equivalent networks...
OverviewCalculus of Collision-proneCommunicating Processes (CCCP)Contextual EquivalenceCoinductive CharacterisationDetermi...
Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities hap...
Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities hap...
Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities hap...
Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities hap...
Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities hap...
CCCP FormallyChannel environment: keepstrack of transmission relatedinformationΓ c : (time, val)System term: contains the ...
CCCP FormallyChannel environment: keepstrack of transmission relatedinformationΓ c : (time, val)System term: contains the ...
CCCP FormallyChannel environment: keepstrack of transmission relatedinformationΓ c : (time, val)System term: contains the ...
Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | ...
Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | ...
Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | ...
Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | ...
Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | ...
Example: CollisionsP1 c!vP2 c!wP3 c?x x ← errΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w...
Example: Failure of SynchronisationP1 c!vP2 c?xP3 c?xΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (0, −)Γ1 σ2.nil...
Example: Failure of SynchronisationP1 c!vP2 c?xP3 c?xΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (0, −)Γ1 σ2.nil...
Example: Failure of SynchronisationP1 c!vP2 c?xP3 c?xΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (0, −)Γ1 σ2.nil...
Example: Failure of SynchronisationP1 c!vP2 c?xP3 c?xΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (0, −)Γ1 σ2.nil...
Example: Failure of SynchronisationP1 c!vP2 c?x x ← vP3 c?x x ← errΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (...
Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ....
Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ....
Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ....
Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ....
Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ....
Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ....
Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ....
Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ....
Basic ObservablesReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevolutions in ...
Reduction Barbed CongruenceReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevol...
Reduction Barbed CongruenceReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevol...
Reduction Barbed CongruenceReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevol...
Reduction Barbed CongruenceReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevol...
Extensional SemanticsProving Γ1 W1 Γ2 W2 directly is difficult (contextuality).Strategy: Give a coinductive characterisation...
Extensional SemanticsProving Γ1 W1 Γ2 W2 directly is difficult (contextuality).Strategy: Give a coinductive characterisation...
Extensional SemanticsProving Γ1 W1 Γ2 W2 directly is difficult (contextuality).Strategy: Give a coinductive characterisation...
Extensional SemanticsProving Γ1 W1 Γ2 W2 directly is difficult (contextuality).Strategy: Give a coinductive characterisation...
BisimulationsBisimulation: largest symmetric relation ≈ such thatΓ1 W1≈ Γ2 W2 and Γ1 W1α⇒ Γ1 W1 implies Γ2 W2α⇒ Γ2 W2with ...
Well-TimednessIs the opposite implication to soundness true?Idea: provide a distinguishing test Wα for each extensional ac...
Well-TimednessIs the opposite implication to soundness true?Idea: provide a distinguishing test Wα for each extensional ac...
Well-TimednessIs the opposite implication to soundness true?Idea: provide a distinguishing test Wα for each extensional ac...
CompletenessIs the opposite implication to soundness true?Theorem (Soundness)Γ1 W1 ≈ Γ2 W2impliesΓ1 W1 Γ2 W2(A. Cerone, M....
CompletenessIs the opposite implication to soundness true?Theorem (Soundness)Γ1 W1 ≈ Γ2 W2impliesΓ1 W1 Γ2 W2For Well-Timed...
Conclusions1 Collision-prone Timed Process Calculus2 Barbed Congruence3 Identification of the activities that can be observ...
Thank you(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 15 / 15
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Modelling Mac-Layer Communication in Wireless Systems (Extended Abstract)

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Modelling Mac-Layer Communication in Wireless Systems (Extended Abstract)

  1. 1. Modelling MAC-Layer Communications in WirelessSystems(Extended Abstract)Andrea Cerone 1,Matthew Hennessy 1 and Massimo Merro 21School of Statistics and Computer Science, Trinity College Dublin2Dipartimento di Informatica, Universita’ di VeronaCOORDINATION 2013 - June 4th, Florence(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 1 / 15
  2. 2. OverviewCalculus of Collision-proneCommunicating Processes (CCCP)Contextual EquivalenceCoinductive Characterisation(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 2 / 15
  3. 3. OverviewCalculus of Collision-proneCommunicating Processes (CCCP)Modelling Networks at the MAC-sublayer ofthe ISO/OSI reference modelContextual EquivalenceCoinductive CharacterisationIssues: Collisions, Failures ofSynchronisations(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 2 / 15
  4. 4. OverviewCalculus of Collision-proneCommunicating Processes (CCCP)Contextual EquivalenceInterchange two equivalent networks in alarger one without affecting the overallbehaviourCoinductive CharacterisationNet1 Net2C[·]Net1C[·]Net2(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 2 / 15
  5. 5. OverviewCalculus of Collision-proneCommunicating Processes (CCCP)Contextual EquivalenceCoinductive CharacterisationDetermining if two networks are equivalentwithout having to quantify over contextsBisimulation (≈) based proofprincipleSoundness:Net1 ≈ Net2 impliesNet1 Net2Completeness :Net1 Net2 impliesNet1 ≈ Net2Holds for all networks satisfyinga natural requirement(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 2 / 15
  6. 6. Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities happen within time slotsTransmission of messages canrequire several time slotsCollision-prone CommunicationError in Reception caused bycollisionsor by missed synchronisations(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15
  7. 7. Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities happen within time slotsTransmission of messages canrequire several time slotsCollision-prone CommunicationError in Reception caused bycollisionsor by missed synchronisationsP1 c!vP2 c!wP3 c?·(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15
  8. 8. Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities happen within time slotsTransmission of messages canrequire several time slotsCollision-prone CommunicationError in Reception caused bycollisionsor by missed synchronisationsP1 c!vP2 c!wP3 c?·(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15
  9. 9. Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities happen within time slotsTransmission of messages canrequire several time slotsCollision-prone CommunicationError in Reception caused bycollisionsor by missed synchronisationsP1 c!vP2 c!wP3 c?x x ←???c!(v, w)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15
  10. 10. Features of CCCPBroadcast CommunicationTransmitted messages can bereceived by multiple stationsDiscrete TimeActivities happen within time slotsTransmission of messages canrequire several time slotsCollision-prone CommunicationError in Reception caused bycollisionsor by missed synchronisationsP1 c!vP2 c?x x ←???P2 : ¬(c?)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15
  11. 11. CCCP FormallyChannel environment: keepstrack of transmission relatedinformationΓ c : (time, val)System term: contains the codeexecuted by stationsW = P1 | · · · | PnEvolution of a network:Γ1 W1 Γ2 W2(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 4 / 15
  12. 12. CCCP FormallyChannel environment: keepstrack of transmission relatedinformationΓ c : (time, val)System term: contains the codeexecuted by stationsW = P1 | · · · | PnEvolution of a network:Γ1 W1 Γ2 W2Constructs:Output c ! v .PTime-out Input c?(x).P QActive Receiver [c ← x]PExposure Check [exp(c)]P, QStandard Constructs(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 4 / 15
  13. 13. CCCP FormallyChannel environment: keepstrack of transmission relatedinformationΓ c : (time, val)System term: contains the codeexecuted by stationsW = P1 | · · · | PnEvolution of a network:Γ1 W1 Γ2 W2i: Instantaneous reduction(within a time slot)σ: Passage of time(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 4 / 15
  14. 14. Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | [c ← x].P σ Γ1 c : (2, v)Γ2 σ.nil | c ! w .nil | [c ← x].P i Γ2 c : (1, v)Γ3 σ.nil | σ2.nil | [c ← x].P σ Γ3 c : (2, err)Γ4 nil | σ.nil | [c ← x].P σ Γ4 c : (1, err)Γ0 nil | nil | {err/x}P Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 5 / 15
  15. 15. Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | [c ← x].P σ Γ1 c : (2, v)Γ2 σ.nil | c ! w .nil | [c ← x].P i Γ2 c : (1, v)Γ3 σ.nil | σ2.nil | [c ← x].P σ Γ3 c : (2, err)Γ4 nil | σ.nil | [c ← x].P σ Γ4 c : (1, err)Γ0 nil | nil | {err/x}P Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 5 / 15
  16. 16. Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | [c ← x].P σ Γ1 c : (2, v)Γ2 σ.nil | c ! w .nil | [c ← x].P i Γ2 c : (1, v)Γ3 σ.nil | σ2.nil | [c ← x].P σ Γ3 c : (2, err)Γ4 nil | σ.nil | [c ← x].P σ Γ4 c : (1, err)Γ0 nil | nil | {err/x}P Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 5 / 15
  17. 17. Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | [c ← x].P σ Γ1 c : (2, v)Γ2 σ.nil | c ! w .nil | [c ← x].P i Γ2 c : (1, v)Γ3 σ.nil | σ2.nil | [c ← x].P σ Γ3 c : (2, err)Γ4 nil | σ.nil | [c ← x].P σ Γ4 c : (1, err)Γ0 nil | nil | {err/x}P Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 5 / 15
  18. 18. Example: CollisionsP1 c!vP2 c!wP3 c?xΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | [c ← x].P σ Γ1 c : (2, v)Γ2 σ.nil | c ! w .nil | [c ← x].P i Γ2 c : (1, v)Γ3 σ.nil | σ2.nil | [c ← x].P σ Γ3 c : (2, err)Γ4 nil | σ.nil | [c ← x].P σ Γ4 c : (1, err)Γ0 nil | nil | {err/x}P Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 5 / 15
  19. 19. Example: CollisionsP1 c!vP2 c!wP3 c?x x ← errΓ0 c ! v .nil | σ.c ! w .nil | c?(x).P nil i Γ0 c : (0, −)Γ1 σ2.nil | σ.c ! w .nil | [c ← x].P σ Γ1 c : (2, v)Γ2 σ.nil | c ! w .nil | [c ← x].P i Γ2 c : (1, v)Γ3 σ.nil | σ2.nil | [c ← x].P σ Γ3 c : (2, err)Γ4 nil | σ.nil | [c ← x].P σ Γ4 c : (1, err)Γ0 nil | nil | {err/x}P Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 5 / 15
  20. 20. Example: Failure of SynchronisationP1 c!vP2 c?xP3 c?xΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (0, −)Γ1 σ2.nil | [c ← x].P | σ. c?(x).Q nil σ Γ1 c : (2, v)Γ2 σ.nil | [c ← x].P | c?(x).Q nil i Γ2 c : (1, v)Γ2 σ.nil | [c ← x].P | [c ← x].{err/x}Q σ Γ2 c : (1, v)Γ0 nil | {v/x}P | {err/x}Q Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 6 / 15
  21. 21. Example: Failure of SynchronisationP1 c!vP2 c?xP3 c?xΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (0, −)Γ1 σ2.nil | [c ← x].P | σ. c?(x).Q nil σ Γ1 c : (2, v)Γ2 σ.nil | [c ← x].P | c?(x).Q nil i Γ2 c : (1, v)Γ2 σ.nil | [c ← x].P | [c ← x].{err/x}Q σ Γ2 c : (1, v)Γ0 nil | {v/x}P | {err/x}Q Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 6 / 15
  22. 22. Example: Failure of SynchronisationP1 c!vP2 c?xP3 c?xΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (0, −)Γ1 σ2.nil | [c ← x].P | σ. c?(x).Q nil σ Γ1 c : (2, v)Γ2 σ.nil | [c ← x].P | c?(x).Q nil i Γ2 c : (1, v)Γ2 σ.nil | [c ← x].P | [c ← x].{err/x}Q σ Γ2 c : (1, v)Γ0 nil | {v/x}P | {err/x}Q Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 6 / 15
  23. 23. Example: Failure of SynchronisationP1 c!vP2 c?xP3 c?xΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (0, −)Γ1 σ2.nil | [c ← x].P | σ. c?(x).Q nil σ Γ1 c : (2, v)Γ2 σ.nil | [c ← x].P | c?(x).Q nil i Γ2 c : (1, v)Γ2 σ.nil | [c ← x].P | [c ← x].{err/x}Q σ Γ2 c : (1, v)Γ0 nil | {v/x}P | {err/x}Q Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 6 / 15
  24. 24. Example: Failure of SynchronisationP1 c!vP2 c?x x ← vP3 c?x x ← errΓ0 c ! v .nil | c?(x).P nil | σ. c?(x).Q nil i Γ0 c : (0, −)Γ1 σ2.nil | [c ← x].P | σ. c?(x).Q nil σ Γ1 c : (2, v)Γ2 σ.nil | [c ← x].P | c?(x).Q nil i Γ2 c : (1, v)Γ2 σ.nil | [c ← x].P | [c ← x].{err/x}Q σ Γ2 c : (1, v)Γ0 nil | {v/x}P | {err/x}Q Γ0 c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 6 / 15
  25. 25. Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ.Q σΓ0 nil | QP1 c!vP2 exp(c) PΓ0 c ! v .nil | [exp(c)]P, Q iΓ1 σ.nil | [exp(c)]P, Q iΓ1 σ.nil | σ.P σΓ0 nil | P(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15
  26. 26. Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ.Q σΓ0 nil | QP1 c!vP2 exp(c) PΓ0 c ! v .nil | [exp(c)]P, Q iΓ1 σ.nil | [exp(c)]P, Q iΓ1 σ.nil | σ.P σΓ0 nil | P(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15
  27. 27. Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ.Q σΓ0 nil | QP1 c!vP2 exp(c) PΓ0 c ! v .nil | [exp(c)]P, Q iΓ1 σ.nil | [exp(c)]P, Q iΓ1 σ.nil | σ.P σΓ0 nil | P(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15
  28. 28. Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ.Q σΓ0 nil | QP1 c!vP2 exp(c) PΓ0 c ! v .nil | [exp(c)]P, Q iΓ1 σ.nil | [exp(c)]P, Q iΓ1 σ.nil | σ.P σΓ0 nil | P(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15
  29. 29. Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ.Q σΓ0 nil | QP1 c!vP2 exp(c) PΓ0 c ! v .nil | [exp(c)]P, Q iΓ1 σ.nil | [exp(c)]P, Q iΓ1 σ.nil | σ.P σΓ0 nil | P(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15
  30. 30. Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ.Q σΓ0 nil | QP1 c!vP2 exp(c) PΓ0 c ! v .nil | [exp(c)]P, Q iΓ1 σ.nil | [exp(c)]P, Q iΓ1 σ.nil | σ.P σΓ0 nil | P(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15
  31. 31. Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ.Q σΓ0 nil | QP1 c!vP2 exp(c) PΓ0 c ! v .nil | [exp(c)]P, Q iΓ1 σ.nil | [exp(c)]P, Q iΓ1 σ.nil | σ.P σΓ0 nil | P(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15
  32. 32. Exposure CheckΓ0 c : (0, −) Γ1 c : (1, v)P1 c!vP2 exp(c) QΓ0 c ! v .nil | [exp(c)]P, Q iΓ0 c ! v .nil | σ.Q iΓ1 σ.nil | σ.Q σΓ0 nil | QP1 c!vP2 exp(c) PΓ0 c ! v .nil | [exp(c)]P, Q iΓ1 σ.nil | [exp(c)]P, Q iΓ1 σ.nil | σ.P σΓ0 nil | P(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15
  33. 33. Basic ObservablesReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevolutions in all possible contextsStandard notion of observable: the ability to output on a channel cObservables in CCCP: a channel c being exposed to a transmissionObservablesΓ W ↓c if Γ c : (n, v), n > 0Γ W ⇓c if Γ W ∗ Γ W ↓c(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 8 / 15
  34. 34. Reduction Barbed CongruenceReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevolutions in all possible contextsReduction barbed congruence: largest symmetric relation which isBarb PreservingReduction ClosedContextual(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 9 / 15
  35. 35. Reduction Barbed CongruenceReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevolutions in all possible contextsReduction barbed congruence: largest symmetric relation which isBarb PreservingReduction ClosedContextualΓ1 W1 Γ2 W2Γ1 W1 ⇓c implies Γ2 W2 ⇓c(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 9 / 15
  36. 36. Reduction Barbed CongruenceReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevolutions in all possible contextsReduction barbed congruence: largest symmetric relation which isBarb PreservingReduction ClosedContextualΓ1 W1 Γ2 W2Γ1 W1∗ Γ1 W1 impliesΓ2 W2∗ Γ2 W2 such thatΓ1 W1 Γ2 W2(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 9 / 15
  37. 37. Reduction Barbed CongruenceReduction Barbed CongruenceΓ1 W1 Γ2 W2 if they have the same observables under all possibleevolutions in all possible contextsReduction barbed congruence: largest symmetric relation which isBarb PreservingReduction ClosedContextualΓ1 W1 Γ2 W2Γ1 W1 | W Γ2 W2 | W(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 9 / 15
  38. 38. Extensional SemanticsProving Γ1 W1 Γ2 W2 directly is difficult (contextuality).Strategy: Give a coinductive characterisation based on the activities ofsystems observable by some contextExtensional Semantics:internal activities:τ→ = iTime:σ→ = σInput:c?v→Idleness:ι(c)→Delivery:γ(c,v)→(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 10 / 15
  39. 39. Extensional SemanticsProving Γ1 W1 Γ2 W2 directly is difficult (contextuality).Strategy: Give a coinductive characterisation based on the activities ofsystems observable by some contextExtensional Semantics:internal activities:τ→ = iTime:σ→ = σInput:c?v→Idleness:ι(c)→Delivery:γ(c,v)→Detecting channel c to be idleΓ c : (0, v)Γ Wι(c)→ Γ W(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 10 / 15
  40. 40. Extensional SemanticsProving Γ1 W1 Γ2 W2 directly is difficult (contextuality).Strategy: Give a coinductive characterisation based on the activities ofsystems observable by some contextExtensional Semantics:internal activities:τ→ = iTime:σ→ = σInput:c?v→Idleness:ι(c)→Delivery:γ(c,v)→Detecting the delivery of value valong channel cΓ W σ Γ W Γ c : (1, v)Γ Wγ(c,v)→ Γ W(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 10 / 15
  41. 41. Extensional SemanticsProving Γ1 W1 Γ2 W2 directly is difficult (contextuality).Strategy: Give a coinductive characterisation based on the activities ofsystems observable by some contextExtensional Semantics:internal activities:τ→ = iTime:σ→ = σInput:c?v→Idleness:ι(c)→Delivery:γ(c,v)→Weak variantα⇒: Abstracting from internal activities(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 10 / 15
  42. 42. BisimulationsBisimulation: largest symmetric relation ≈ such thatΓ1 W1≈ Γ2 W2 and Γ1 W1α⇒ Γ1 W1 implies Γ2 W2α⇒ Γ2 W2with Γ1 W1 ≈ Γ2 W2Theorem (Soundness)Γ1 W1 ≈ Γ2 W2 implies Γ1 W1 Γ2 W2Remark:ι(c)⇒ andγ(c,v)⇒ actions necessary for achieving soundness(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 11 / 15
  43. 43. Well-TimednessIs the opposite implication to soundness true?Idea: provide a distinguishing test Wα for each extensional actionα⇒(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 12 / 15
  44. 44. Well-TimednessIs the opposite implication to soundness true?Idea: provide a distinguishing test Wα for each extensional actionα⇒Several time slots are required to detect whether the actionα⇒ has beenperformedBut some systems do not allow time to pass!Γ [c ← x].P σ if Γ c : (0, −)(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 12 / 15
  45. 45. Well-TimednessIs the opposite implication to soundness true?Idea: provide a distinguishing test Wα for each extensional actionα⇒Several time slots are required to detect whether the actionα⇒ has beenperformedBut some systems do not allow time to pass!Γ [c ← x].P σ if Γ c : (0, −)Well-TimednessΓ W ∗ Γ1 W1 implies Γ1 W1∗ Γ2 W2 σNatural RequirementCan be checked syntactically(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 12 / 15
  46. 46. CompletenessIs the opposite implication to soundness true?Theorem (Soundness)Γ1 W1 ≈ Γ2 W2impliesΓ1 W1 Γ2 W2(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 13 / 15
  47. 47. CompletenessIs the opposite implication to soundness true?Theorem (Soundness)Γ1 W1 ≈ Γ2 W2impliesΓ1 W1 Γ2 W2For Well-Timed systems:Theorem (Completeness)Γ1 W1 Γ2 W2impliesΓ1 W1 ≈ Γ2 W2(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 13 / 15
  48. 48. Conclusions1 Collision-prone Timed Process Calculus2 Barbed Congruence3 Identification of the activities that can be observed4 Full abstraction (for systems satisfying a natural requirement)result achieved for the first time(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 14 / 15
  49. 49. Thank you(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 15 / 15

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