Presentation of the paper at Coordination 2013, part of the federated event DisCoTec 2013. The paper was awarded the "best paper" prize.

1. Modelling MAC-Layer Communications in Wireless
Systems
(Extended Abstract)
Andrea Cerone 1,Matthew Hennessy 1 and Massimo Merro 2
1School of Statistics and Computer Science, Trinity College Dublin
2Dipartimento di Informatica, Universita’ di Verona
COORDINATION 2013 - June 4th, Florence
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 1 / 15

2. Overview
Calculus of Collision-prone
Communicating Processes (CCCP)
Contextual Equivalence
Coinductive Characterisation
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 2 / 15

3. Overview
Calculus of Collision-prone
Communicating Processes (CCCP)
Modelling Networks at the MAC-sublayer of
the ISO/OSI reference model
Contextual Equivalence
Coinductive Characterisation
Issues: Collisions, Failures of
Synchronisations
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 2 / 15

4. Overview
Calculus of Collision-prone
Communicating Processes (CCCP)
Contextual Equivalence
Interchange two equivalent networks in a
larger one without affecting the overall
behaviour
Coinductive Characterisation
Net1 Net2
C[·]
Net1
C[·]
Net2
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 2 / 15

5. Overview
Calculus of Collision-prone
Communicating Processes (CCCP)
Contextual Equivalence
Coinductive Characterisation
Determining if two networks are equivalent
without having to quantify over contexts
Bisimulation (≈) based proof
principle
Soundness:
Net1 ≈ Net2 implies
Net1 Net2
Completeness :
Net1 Net2 implies
Net1 ≈ Net2
Holds for all networks satisfying
a natural requirement
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 2 / 15

6. Features of CCCP
Broadcast Communication
Transmitted messages can be
received by multiple stations
Discrete Time
Activities happen within time slots
Transmission of messages can
require several time slots
Collision-prone Communication
Error in Reception caused by
collisions
or by missed synchronisations
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15

7. Features of CCCP
Broadcast Communication
Transmitted messages can be
received by multiple stations
Discrete Time
Activities happen within time slots
Transmission of messages can
require several time slots
Collision-prone Communication
Error in Reception caused by
collisions
or by missed synchronisations
P1 c!v
P2 c!w
P3 c?·
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15

8. Features of CCCP
Broadcast Communication
Transmitted messages can be
received by multiple stations
Discrete Time
Activities happen within time slots
Transmission of messages can
require several time slots
Collision-prone Communication
Error in Reception caused by
collisions
or by missed synchronisations
P1 c!v
P2 c!w
P3 c?·
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15

9. Features of CCCP
Broadcast Communication
Transmitted messages can be
received by multiple stations
Discrete Time
Activities happen within time slots
Transmission of messages can
require several time slots
Collision-prone Communication
Error in Reception caused by
collisions
or by missed synchronisations
P1 c!v
P2 c!w
P3 c?x x ←???
c!(v, w)
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15

10. Features of CCCP
Broadcast Communication
Transmitted messages can be
received by multiple stations
Discrete Time
Activities happen within time slots
Transmission of messages can
require several time slots
Collision-prone Communication
Error in Reception caused by
collisions
or by missed synchronisations
P1 c!v
P2 c?x x ←???
P2 : ¬(c?)
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 3 / 15

11. CCCP Formally
Channel environment: keeps
track of transmission related
information
Γ c : (time, val)
System term: contains the code
executed by stations
W = P1 | · · · | Pn
Evolution of a network:
Γ1 W1 Γ2 W2
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 4 / 15

12. CCCP Formally
Channel environment: keeps
track of transmission related
information
Γ c : (time, val)
System term: contains the code
executed by stations
W = P1 | · · · | Pn
Evolution of a network:
Γ1 W1 Γ2 W2
Constructs:
Output c ! v .P
Time-out Input c?(x).P Q
Active Receiver [c ← x]P
Exposure Check [exp(c)]P, Q
Standard Constructs
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 4 / 15

13. CCCP Formally
Channel environment: keeps
track of transmission related
information
Γ c : (time, val)
System term: contains the code
executed by stations
W = P1 | · · · | Pn
Evolution of a network:
Γ1 W1 Γ2 W2
i: 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. Example: Collisions
P1 c!v
P2 c!w
P3 c?x
Γ0 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. Example: Collisions
P1 c!v
P2 c!w
P3 c?x
Γ0 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. Example: Collisions
P1 c!v
P2 c!w
P3 c?x
Γ0 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. Example: Collisions
P1 c!v
P2 c!w
P3 c?x
Γ0 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. Example: Collisions
P1 c!v
P2 c!w
P3 c?x
Γ0 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. Example: Collisions
P1 c!v
P2 c!w
P3 c?x x ← err
Γ0 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. Example: Failure of Synchronisation
P1 c!v
P2 c?x
P3 c?x
Γ0 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. Example: Failure of Synchronisation
P1 c!v
P2 c?x
P3 c?x
Γ0 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. Example: Failure of Synchronisation
P1 c!v
P2 c?x
P3 c?x
Γ0 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. Example: Failure of Synchronisation
P1 c!v
P2 c?x
P3 c?x
Γ0 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. Example: Failure of Synchronisation
P1 c!v
P2 c?x x ← v
P3 c?x x ← err
Γ0 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. Exposure Check
Γ0 c : (0, −) Γ1 c : (1, v)
P1 c!v
P2 exp(c) Q
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ0 c ! v .nil | σ.Q i
Γ1 σ.nil | σ.Q σ
Γ0 nil | Q
P1 c!v
P2 exp(c) P
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ1 σ.nil | [exp(c)]P, Q i
Γ1 σ.nil | σ.P σ
Γ0 nil | P
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15

26. Exposure Check
Γ0 c : (0, −) Γ1 c : (1, v)
P1 c!v
P2 exp(c) Q
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ0 c ! v .nil | σ.Q i
Γ1 σ.nil | σ.Q σ
Γ0 nil | Q
P1 c!v
P2 exp(c) P
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ1 σ.nil | [exp(c)]P, Q i
Γ1 σ.nil | σ.P σ
Γ0 nil | P
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15

27. Exposure Check
Γ0 c : (0, −) Γ1 c : (1, v)
P1 c!v
P2 exp(c) Q
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ0 c ! v .nil | σ.Q i
Γ1 σ.nil | σ.Q σ
Γ0 nil | Q
P1 c!v
P2 exp(c) P
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ1 σ.nil | [exp(c)]P, Q i
Γ1 σ.nil | σ.P σ
Γ0 nil | P
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15

28. Exposure Check
Γ0 c : (0, −) Γ1 c : (1, v)
P1 c!v
P2 exp(c) Q
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ0 c ! v .nil | σ.Q i
Γ1 σ.nil | σ.Q σ
Γ0 nil | Q
P1 c!v
P2 exp(c) P
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ1 σ.nil | [exp(c)]P, Q i
Γ1 σ.nil | σ.P σ
Γ0 nil | P
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15

29. Exposure Check
Γ0 c : (0, −) Γ1 c : (1, v)
P1 c!v
P2 exp(c) Q
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ0 c ! v .nil | σ.Q i
Γ1 σ.nil | σ.Q σ
Γ0 nil | Q
P1 c!v
P2 exp(c) P
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ1 σ.nil | [exp(c)]P, Q i
Γ1 σ.nil | σ.P σ
Γ0 nil | P
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15

30. Exposure Check
Γ0 c : (0, −) Γ1 c : (1, v)
P1 c!v
P2 exp(c) Q
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ0 c ! v .nil | σ.Q i
Γ1 σ.nil | σ.Q σ
Γ0 nil | Q
P1 c!v
P2 exp(c) P
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ1 σ.nil | [exp(c)]P, Q i
Γ1 σ.nil | σ.P σ
Γ0 nil | P
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15

31. Exposure Check
Γ0 c : (0, −) Γ1 c : (1, v)
P1 c!v
P2 exp(c) Q
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ0 c ! v .nil | σ.Q i
Γ1 σ.nil | σ.Q σ
Γ0 nil | Q
P1 c!v
P2 exp(c) P
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ1 σ.nil | [exp(c)]P, Q i
Γ1 σ.nil | σ.P σ
Γ0 nil | P
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15

32. Exposure Check
Γ0 c : (0, −) Γ1 c : (1, v)
P1 c!v
P2 exp(c) Q
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ0 c ! v .nil | σ.Q i
Γ1 σ.nil | σ.Q σ
Γ0 nil | Q
P1 c!v
P2 exp(c) P
Γ0 c ! v .nil | [exp(c)]P, Q i
Γ1 σ.nil | [exp(c)]P, Q i
Γ1 σ.nil | σ.P σ
Γ0 nil | P
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 7 / 15

33. Basic Observables
Reduction Barbed Congruence
Γ1 W1 Γ2 W2 if they have the same observables under all possible
evolutions in all possible contexts
Standard notion of observable: the ability to output on a channel c
Observables in CCCP: a channel c being exposed to a transmission
Observables
Γ W ↓c if Γ c : (n, v), n > 0
Γ W ⇓c if Γ W ∗ Γ W ↓c
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 8 / 15

34. Reduction Barbed Congruence
Reduction Barbed Congruence
Γ1 W1 Γ2 W2 if they have the same observables under all possible
evolutions in all possible contexts
Reduction barbed congruence: largest symmetric relation which is
Barb Preserving
Reduction Closed
Contextual
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 9 / 15

35. Reduction Barbed Congruence
Reduction Barbed Congruence
Γ1 W1 Γ2 W2 if they have the same observables under all possible
evolutions in all possible contexts
Reduction barbed congruence: largest symmetric relation which is
Barb Preserving
Reduction Closed
Contextual
Γ1 W1 Γ2 W2
Γ1 W1 ⇓c implies Γ2 W2 ⇓c
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 9 / 15

36. Reduction Barbed Congruence
Reduction Barbed Congruence
Γ1 W1 Γ2 W2 if they have the same observables under all possible
evolutions in all possible contexts
Reduction barbed congruence: largest symmetric relation which is
Barb Preserving
Reduction Closed
Contextual
Γ1 W1 Γ2 W2
Γ1 W1
∗ Γ1 W1 implies
Γ2 W2
∗ Γ2 W2 such that
Γ1 W1 Γ2 W2
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 9 / 15

37. Reduction Barbed Congruence
Reduction Barbed Congruence
Γ1 W1 Γ2 W2 if they have the same observables under all possible
evolutions in all possible contexts
Reduction barbed congruence: largest symmetric relation which is
Barb Preserving
Reduction Closed
Contextual
Γ1 W1 Γ2 W2
Γ1 W1 | W Γ2 W2 | W
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 9 / 15

38. Extensional Semantics
Proving Γ1 W1 Γ2 W2 directly is difficult (contextuality).
Strategy: Give a coinductive characterisation based on the activities of
systems observable by some context
Extensional Semantics:
internal activities:
τ
→ = i
Time:
σ
→ = σ
Input:
c?v
→
Idleness:
ι(c)
→
Delivery:
γ(c,v)
→
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 10 / 15

39. Extensional Semantics
Proving Γ1 W1 Γ2 W2 directly is difficult (contextuality).
Strategy: Give a coinductive characterisation based on the activities of
systems observable by some context
Extensional Semantics:
internal activities:
τ
→ = i
Time:
σ
→ = σ
Input:
c?v
→
Idleness:
ι(c)
→
Delivery:
γ(c,v)
→
Detecting channel c to be idle
Γ c : (0, v)
Γ W
ι(c)
→ Γ W
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 10 / 15

40. Extensional Semantics
Proving Γ1 W1 Γ2 W2 directly is difficult (contextuality).
Strategy: Give a coinductive characterisation based on the activities of
systems observable by some context
Extensional Semantics:
internal activities:
τ
→ = i
Time:
σ
→ = σ
Input:
c?v
→
Idleness:
ι(c)
→
Delivery:
γ(c,v)
→
Detecting the delivery of value v
along channel c
Γ W σ Γ W Γ c : (1, v)
Γ W
γ(c,v)
→ Γ W
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 10 / 15

41. Extensional Semantics
Proving Γ1 W1 Γ2 W2 directly is difficult (contextuality).
Strategy: Give a coinductive characterisation based on the activities of
systems observable by some context
Extensional Semantics:
internal activities:
τ
→ = i
Time:
σ
→ = σ
Input:
c?v
→
Idleness:
ι(c)
→
Delivery:
γ(c,v)
→
Weak variant
α
⇒: Abstracting from internal activities
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 10 / 15

42. Bisimulations
Bisimulation: largest symmetric relation ≈ such that
Γ1 W1≈ Γ2 W2 and Γ1 W1
α
⇒ Γ1 W1 implies Γ2 W2
α
⇒ Γ2 W2
with Γ1 W1 ≈ Γ2 W2
Theorem (Soundness)
Γ1 W1 ≈ Γ2 W2 implies Γ1 W1 Γ2 W2
Remark:
ι(c)
⇒ and
γ(c,v)
⇒ actions necessary for achieving soundness
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 11 / 15

43. Well-Timedness
Is the opposite implication to soundness true?
Idea: provide a distinguishing test Wα for each extensional action
α
⇒
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 12 / 15

44. Well-Timedness
Is the opposite implication to soundness true?
Idea: provide a distinguishing test Wα for each extensional action
α
⇒
Several time slots are required to detect whether the action
α
⇒ has been
performed
But 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. Well-Timedness
Is the opposite implication to soundness true?
Idea: provide a distinguishing test Wα for each extensional action
α
⇒
Several time slots are required to detect whether the action
α
⇒ has been
performed
But some systems do not allow time to pass!
Γ [c ← x].P σ if Γ c : (0, −)
Well-Timedness
Γ W ∗ Γ1 W1 implies Γ1 W1
∗ Γ2 W2 σ
Natural Requirement
Can be checked syntactically
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 12 / 15

46. Completeness
Is the opposite implication to soundness true?
Theorem (Soundness)
Γ1 W1 ≈ Γ2 W2
implies
Γ1 W1 Γ2 W2
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 13 / 15

47. Completeness
Is the opposite implication to soundness true?
Theorem (Soundness)
Γ1 W1 ≈ Γ2 W2
implies
Γ1 W1 Γ2 W2
For Well-Timed systems:
Theorem (Completeness)
Γ1 W1 Γ2 W2
implies
Γ1 W1 ≈ Γ2 W2
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 13 / 15

48. Conclusions
1 Collision-prone Timed Process Calculus
2 Barbed Congruence
3 Identification of the activities that can be observed
4 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. Thank you
(A. Cerone, M.Hennessy, M.Merro) Collision Prone Communicating Processes COORDINATION ’13 15 / 15