useful to learn about cn

1. Theoretical Foundations
▸Clocks
▹Logical clocks (Lamport)
▹Partially ordered clocks (Fidge)
▸Causally ordered message delivery
▹Broadcast-based (Birman et al.)
▹Unicast-based (Raynal, Schiper & Toueg)
▸System states
▹Global snapshots (Chandy & Lamport)
▹Termination detection (Huang)
Theoretical Foundations
1

2. Basics of Message Delivery
▸sendp(m)
▹Transmission of message m by process p to a set of
destinations denoted destinations(m)
▸receiveq(m)
▹Reception of message m by process q
▹sendp(m)  receiveq(m)
▸deliverq(m)
▹Delivery of message m to process q
▹receiveq(m)  deliverq(m)
Theoretical Foundations > Causal Delivery
2

3. Causal Delivery
▸Causal Delivery:
▹If sendi(w)  sendj(m), and
q ∈ destinations(w) and q ∈ destinations(m),
then deliverq(w)  deliverq(m)
▸What’s an example of a causal delivery protocol?
▹Transmission Control Protocol (TCP)
Theoretical Foundations > Causal Delivery
3

4. Broadcast-based Causal Delivery
▸Broadcast:
▹when a process sends a message, it sends the
message to every process in the system
▹Called a multicast when sending to a defined group
Theoretical Foundations > Causal Delivery > Broadcast-based
4

5. BSS Protocol
▸Broadcast-based causal delivery protocol
▹Assumes an external service implements group
abstraction
▹sendp(m) broadcasts message m to the entire group in a
single action
▸Assumes a lossless network
▹Any message broadcast will eventually be received unless
the sender or destination fail
▸Assumes a failure detection mechanism exists
▹Will remove failed processes from the group
▹Will flush broadcasts at the time of a failure
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
5

6. BSS Protocol Rules
▸Rule 1
Before sending message m, process i increments
Ci[i] and timestamps m.
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
6

7. BSS Protocol Rules
▸Rule 2
On reception of message m sent by process i and
timestamped tm, process j (≠ i) delays delivery of
m until:
∀k:[1…n]
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
7
tm[k] = Cj[k] + 1; if k = i
tm[k] ≤ Cj[k]; if k ≠ i

8. BSS Protocol Rules
▸Rule 3
When a message m is delivered, Cj is updated to
max(Cj, tm).
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
8

9. BSS Safety and Liveness
▸Safety:
▹messages are always delivered in causal order
▹Causal delivery is never violated
▸Liveness:
▹a message will never be indefinitely delayed
▹Every message will be delivered eventually
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
9

10. BSS Protocol Exercise
▸Rule 1: i increments Ci[i] and timestamps m
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
10
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]

11. BSS Protocol Exercise
▸Rule 1: i increments Ci[i] and timestamps m
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
11
P
Q
R
[1 0 0]
[0 0 0]
[0 0 0]
[1 0 0]

12. BSS Protocol Exercise
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
12
P
Q
R
[1 0 0]
[0 0 0]
[0 0 0]
[1 0 0]

13. BSS Protocol Exercise
▸Rule 1: i increments Ci[i] and timestamps m
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
13
P
Q
R
[1 0 0]
[0 0 0]
[0 0 1]
[1 0 0]
[0 0 1]

14. BSS Protocol Exercise
▸Rule 2: Delivery the message
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
14
P
Q
R
[1 0 0]
[0 0 0]
[0 0 1]
[1 0 0]
[0 0 1]

15. BSS Protocol Exercise
▸Rule 3: Cj is updated to max(Cj, tm)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
15
P
Q
R
[1 0 0]
[1 0 0]
[0 0 1]
[1 0 0]
[0 0 1]

16. BSS Protocol Exercise
▸Rule 2: Delivery the message
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
16
P
Q
R
[1 0 0]
[1 0 0]
[0 0 1]
[1 0 0]
[0 0 1]

17. BSS Protocol Exercise
▸Rule 3: Cj is updated to max(Cj, tm)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
17
P
Q
R
[1 0 1]
[1 0 0]
[0 0 1]
[1 0 0]
[0 0 1]

18. BSS Protocol Exercise
▸Rule 2: Delivery the message
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
18
P
Q
R
[1 0 1]
[1 0 0]
[0 0 1]
[1 0 0]
[0 0 1]

19. BSS Protocol Exercise
▸Rule 3: Cj is updated to max(Cj, tm)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
19
P
Q
R
[1 0 1]
[1 0 1]
[0 0 1]
[1 0 0]
[0 0 1]

20. BSS Protocol Exercise
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
20
P
Q
R
[1 0 1]
[1 0 1]
[0 0 1]
[1 0 0]
[0 0 1]

21. BSS Protocol Exercise
▸Rule 1: i increments Ci[i] and timestamps m
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
21
P
Q
R
[1 0 1]
[1 1 1]
[0 0 1]
[1 0 0]
[0 0 1]
[1 1 1]
[1 1 1]

22. BSS Protocol Exercise
▸Rule 2: Delivery the message
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
22
P
Q
R
[1 0 1]
[1 1 1]
[0 0 1]
[1 0 0]
[0 0 1]
[1 1 1]
[1 1 1]

23. BSS Protocol Exercise
▸Rule 3: Cj is updated to max(Cj, tm)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
23
P
Q
R
[1 1 1]
[1 1 1]
[0 0 1]
[1 0 0]
[0 0 1]
[1 1 1]
[1 1 1]

24. BSS Protocol Exercise
▸Rule 2: Delay delivering the message
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
24
P
Q
R
[1 1 1]
[1 1 1]
[0 0 1]
[1 0 0]
[0 0 1]
[1 1 1]
[1 1 1]

25. BSS Protocol Exercise
▸Rule 2: Deliver the message
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
25
P
Q
R
[1 1 1]
[1 1 1]
[0 0 1]
[1 0 0]
[0 0 1]
[1 1 1]
[1 1 1]

26. BSS Protocol Exercise
▸Rule 3: Cj is updated to max(Cj, tm)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
26
P
Q
R
[1 1 1]
[1 1 1]
[1 0 1]
[1 0 0]
[0 0 1]
[1 1 1]
[1 1 1]

27. BSS Protocol Exercise
▸Rule 2: Check the buffer for delayed messages
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
27
P
Q
R
[1 1 1]
[1 1 1]
[1 0 1]
[1 0 0]
[0 0 1]
[1 1 1]
[1 1 1]

28. BSS Protocol Exercise
▸Rule 2: Deliver the message
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
28
P
Q
R
[1 1 1]
[1 1 1]
[1 0 1]
[1 0 0]
[0 0 1]
[1 1 1]
[1 1 1]

29. BSS Protocol Exercise
▸Rule 3: Cj is updated to max(Cj, tm)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
29
P
Q
R
[1 1 1]
[1 1 1]
[1 1 1]
[1 0 0]
[0 0 1]
[1 1 1]
[1 1 1]

30. Proof of BSS Safety
▸Safety:
▹messages are always delivered in causal order
▹Causal delivery is never violated
▸Must prove
▹If send(m1)  send(m2)
then deliveri(m1)  deliveri(m2)
▹Two cases:
1. Same process: sendp(m1)  sendp(m2)
2. Different processes: sendp(m1)  sendq(m2)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
30

31. Proof of BSS Safety: Case 1
▸If sendp(m1)  sendp(m2) then deliveri(m1)  deliveri(m2)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
31
P
Q
R
[2 1 0]
[2 1 0]
[2 1 0]
[1 0 0] [2 0 0]
[1 1 0]
[1 1 0]

32. Proof of BSS Safety: Case 2
▸If sendp(m1)  sendq(m2) then deliveri(m1)  deliveri(m2)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
32
X
Y
Z
create(R1)
create(R1)
update(R1)
R1
R1
R1
R1
R1
[1 1 0]
[1 1 0]
[1 1 0]
[0 1 0]
[0 1 0]
[1 1 0]
R1

33. Quiz Question
▸Assume sentQ(m)  sentQ(n),
process P ∈ dests(m), and P ∈ dests(n).
If deliverP(n)  deliverP(m), then safety is
violated.
▹True
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
33

34. Proof of BSS Liveness
▸Liveness:
▹a message will never be indefinitely delayed
▹Every message will be delivered eventually
▸Must prove
▹If sendi(m) and receivej(m) then deliverj(m)
▹Two counterexamples:
1. If k = i then tm[k] will never equal Cj[k] + 1
2. If k ≠ i then tm[k] will always be greater than Cj[k]
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
34

35. Proof of BSS Liveness: Counterexample 1
▸If k = i then tm[k] will never equal Cj[k] + 1
▸tm[k] is not less than Cj[k] + 1
▹Process i sent message m
▹Hence, Cj[i] < Ci[i] when m was timestamped
▸If tm[k] is more than Cj[k] + 1
▹Process i sent other messages prior to m
▸BSS assumes a lossless network
▹Process j will eventually receive the other messages from i
▹Hence, tm[k] will eventually equal Cj[k] + 1
▸Proves if sendi(m) and receivej(m) then deliverj(m)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
35

36. Proof of BSS Liveness: Counterexample 2
▸If k ≠ i then tm[k] will always be greater than Cj[k]
▸tm[k] is greater than Cj[k]
▹Before sending message m to process j,
process i received messages from process k that process j
has not received
▸BSS is broadcast-based
▹Process k also sent these messages to process j
▸BSS assumes a lossless network
▹Process j will eventually receive the messages from k
▹Hence, tm[k] will eventually be less than or equal to Cj[k]
▸Proves if sendi(m) and receivej(m) then deliverj(m)
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
36

37. Quiz Question
▸Assume sentQ(m)  sentQ(n),
process P ∈ dests(m), and P ∈ dests(n).
If deliverP(m) never occurs, then liveness is
violated.
▹True
Theoretical Foundations > Causal Delivery > Broadcast-based > BSS Protocol
37

38. Theoretical Foundations
▸Clocks
▹Logical clocks (Lamport)
▹Partially ordered clocks (Fidge)
▸Causally ordered message delivery
▹Broadcast-based (Birman et al.)
▹Unicast-based (Raynal, Schiper & Toueg)
▸System states
▹Global snapshots (Chandy & Lamport)
▹Termination detection (Huang)
Theoretical Foundations
38

39. Theoretical Foundations:
Unicast-based Causal Delivery
CS/CE/TE 6378
Advanced Operating Systems

40. Unicast-based Causal Delivery
▸Unicast:
▹when a process sends a message, it sends the
message to one process in the system
Theoretical Foundations > Causal Delivery > Unicast-based
40

41. RST Protocol
▸RST:
▹Raynal, Schiper & Toueg
▸A causal delivery protocol
▹Uses matrices to track messages sent
▸Assumes a lossless network
▹Any message unicast will eventually be received
unless the sender or destination fail
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
41

42. RST Protocol Variables
▸Every process manages two variables
▹DELIVj[i]
▸An array [1…n] that represents the number of messages
sent from process i and delivered to process j
▹SENTj[k, l]
▸A matrix [n x n] that represents the number of messages
sent from process k to process l (not necessarily delivered)
from process j’s perspective
▸Both are initialized with 0s
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
42

43. RST Protocol Rules
▸Rule 1
After sending message m to process j with a
copy of SENTi (called tm), process i increments
SENTi[i, j].
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
43

44. RST Protocol Example
▸Rule 1: Timestamp message with current SENT
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
44
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0

45. RST Protocol Example
▸Rule 1: Increment SENTi[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
45
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0

46. RST Protocol Example
▸Rule 1: Timestamp message with current SENT
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
46
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0

47. RST Protocol Example
▸Rule 1: Increment SENTi[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
47
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0

48. RST Protocol Rules
▸Rule 2
On reception of message m from process i and
piggybacked with tm, process j delays delivery
of m until:
∀k:[1…n] tm[k, j] ≤ DELIVj[k]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
48

49. RST Protocol Example
▸Rule 2: j = 0; k = 0; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
49
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
Yes, 0 ≤ 0

50. RST Protocol Example
▸Rule 2: j = 0; k = 1; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
50
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
Yes, 0 ≤ 0

51. RST Protocol Example
▸Rule 2: j = 0; k = 2; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
51
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
Yes, 0 ≤ 0

52. RST Protocol Example
▸Rule 2: Deliver the message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
52
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0

53. RST Protocol Rules
▸Rule 3
On delivery of message m from process i and
piggybacked with tm, process j
1. Increments DELIVj[i],
2. Increments SENTj[i, j],
3. ∀k:[1…n] l:[1…n]
SENTj[k, l] = max(SENTj[k, l], tm[k, l])
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
53

54. RST Protocol Example
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
54
P
Q
R
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0

55. RST Protocol Example
▸Rule 3: Increment DELIVj[i]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
55
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0

56. RST Protocol Example
▸Rule 3: Increment SENTj[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
56
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 0
1 0 0
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0

57. RST Protocol Example
▸Rule 3: max(SENTj, tm)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
57
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0

58. RST Protocol Example
▸Rule 1: Timestamp message with current SENT
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
58
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0

59. RST Protocol Example
▸Rule 1: Increment SENTi[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
59
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 0
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0

60. RST Protocol Example
▸Rule 1: Timestamp message with current SENT
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
60
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 0
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

61. RST Protocol Example
▸Rule 1: Increment SENTi[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
61
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

62. RST Protocol Example
▸Rule 2: j = 2; k = 0; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
62
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 0 ≤ 0

63. RST Protocol Example
▸Rule 2: j = 2; k = 1; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
63
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
No, 1 ≤ 0
/

64. RST Protocol Example
▸Rule 2: Delay delivering the message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
64
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

65. RST Protocol Example
▸Rule 2: j = 2; k = 0; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
65
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 0 ≤ 0

66. RST Protocol Example
▸Rule 2: j = 2; k = 1; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
66
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
No, 1 ≤ 0
/

67. RST Protocol Example
▸Rule 2: Delay delivering the message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
67
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

68. RST Protocol Example
▸Rule 2: j = 2; k = 0; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
68
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 0 ≤ 0

69. RST Protocol Example
▸Rule 2: j = 2; k = 1; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
69
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 0 ≤ 0

70. RST Protocol Example
▸Rule 2: j = 2; k = 2; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
70
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 0 ≤ 0

71. RST Protocol Example
▸Rule 2: Deliver the message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
71
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

72. RST Protocol Example
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
72
P
Q
R
[0 1 0]
[0 0 0]
[0 0 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

73. RST Protocol Example
▸Rule 3: Increment DELIVj[i]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
73
P
Q
R
[0 1 0]
[0 0 0]
[0 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

74. RST Protocol Example
▸Rule 3: Increment SENTj[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
74
P
Q
R
[0 1 0]
[0 0 0]
[0 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

75. RST Protocol Example
▸Rule 3: max(SENTj, tm)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
75
P
Q
R
[0 1 0]
[0 0 0]
[0 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

76. RST Protocol Example
▸Rule 2: j = 2; k = 0; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
76
P
Q
R
[0 1 0]
[0 0 0]
[0 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 0 ≤ 0

77. RST Protocol Example
▸Rule 2: j = 2; k = 1; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
77
P
Q
R
[0 1 0]
[0 0 0]
[0 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 1 ≤ 1

78. RST Protocol Example
▸Rule 2: j = 2; k = 2; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
78
P
Q
R
[0 1 0]
[0 0 0]
[0 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 0 ≤ 0

79. RST Protocol Example
▸Rule 2: Deliver the message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
79
P
Q
R
[0 1 0]
[0 0 0]
[0 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

80. RST Protocol Example
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
80
P
Q
R
[0 1 0]
[0 0 0]
[0 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

81. RST Protocol Example
▸Rule 3: Increment DELIVj[i]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
81
P
Q
R
[0 1 0]
[0 0 0]
[1 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

82. RST Protocol Example
▸Rule 3: Increment SENTj[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
82
P
Q
R
[0 1 0]
[0 0 0]
[1 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

83. RST Protocol Example
▸Rule 3: max(SENTj, tm)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
83
P
Q
R
[0 1 0]
[0 0 0]
[1 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

84. RST Protocol Example
▸Rule 2: j = 2; k = 0; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
84
P
Q
R
[0 1 0]
[0 0 0]
[1 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 0 ≤ 1

85. RST Protocol Example
▸Rule 2: j = 2; k = 1; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
85
P
Q
R
[0 1 0]
[0 0 0]
[1 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 1 ≤ 1

86. RST Protocol Example
▸Rule 2: j = 2; k = 2; tm[k, j] ≤ DELIVj[k]?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
86
P
Q
R
[0 1 0]
[0 0 0]
[1 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0
Yes, 0 ≤ 0

87. RST Protocol Example
▸Rule 2: Deliver the message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
87
P
Q
R
[0 1 0]
[0 0 0]
[1 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

88. RST Protocol Example
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
88
P
Q
R
[0 1 0]
[0 0 0]
[1 1 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

89. RST Protocol Example
▸Rule 3: Increment DELIVj[i]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
89
P
Q
R
[0 1 0]
[0 0 0]
[1 2 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

90. RST Protocol Example
▸Rule 3: Increment SENTj[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
90
P
Q
R
[0 1 0]
[0 0 0]
[1 2 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

91. RST Protocol Example
▸Rule 3: max(SENTj, tm)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
91
P
Q
R
[0 1 0]
[0 0 0]
[1 2 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

92. Quiz Questions
▸Rule 1: Timestamp message with current SENT
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
92
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0

93. Quiz Questions
▸What is the value of the SENT variable attached to m1?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
93
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0

94. Quiz Questions
▸Rule 1: Increment SENTi[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
94
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
0 0 0

95. Quiz Questions
▸Rule 1: Timestamp message with current SENT
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
95
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0

96. Quiz Questions
▸Rule 1: Increment SENTi[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
96
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0

97. Quiz Questions
▸Rule 2: Deliver the message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
97
[0 0 0]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0

98. Quiz Questions
▸Rule 3: Increment DELIVj[i]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
98
[0 0 1]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0

99. Quiz Questions
▸Rule 3: Increment SENTj[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
99
[0 0 1]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0

100. Quiz Questions
▸Rule 3: max(SENTj, tm)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
100
[0 0 1]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0

101. Quiz Questions
▸What is the value of P’s SENT variable after p1?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
101
[0 0 1]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0

102. Quiz Questions
▸Rule 1: Timestamp message with current SENT
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
102
[0 0 1]
[0 0 0]
[0 0 0]
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

103. Quiz Questions
▸Rule 1: Increment SENTi[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
103
[0 0 1]
[0 0 0]
[0 0 0]
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

104. Quiz Questions
▸What is the value of the SENT variable attached to m3?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
104
[0 0 1]
[0 0 0]
[0 0 0]
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

105. Quiz Questions
▸Rule 2: Delay delivering the message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
105
[0 0 1]
[0 0 0]
[0 0 0]
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

106. Quiz Questions
▸What is the value of Q’s DELIV variable after q1?
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
106
[0 0 1]
[0 0 0]
[0 0 0]
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

107. Quiz Questions
▸Rule 2: Deliver the message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
107
[0 0 1]
[0 0 0]
[0 0 0]
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

108. Quiz Questions
▸Rule 3: Increment DELIVj[i]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
108
[0 0 1]
[0 0 1]
[0 0 0]
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

109. Quiz Questions
▸Rule 3: Increment SENTj[i, j]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
109
[0 0 1]
[0 0 1]
[0 0 0]
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

110. Quiz Questions
▸Rule 3: max(SENTj, tm)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
110
[0 0 1]
[0 0 1]
[0 0 0]
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

111. Quiz Questions
▸Rule 2: Deliver the delayed message
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
111
[0 0 1]
[0 0 1]
[0 0 0]
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
1 1 0

112. Proof of RST Safety
▸Safety:
▹messages are always delivered in causal order
▹Causal delivery is never violated
▸Must prove
▹If send(m1)  send(m2)
then deliveri(m1)  deliveri(m2)
▹Two cases:
1. Same process: sendp(m1)  sendp(m2)
2. Different processes: sendp(m1)  sendq(m2)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
112

113. Proof of RST Safety: Case 1
▸If sendp(m1)  sendp(m2) then deliveri(m1)  deliveri(m2)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
113
P
Q
R
[0 1 0]
[0 0 0]
[1 2 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

114. Proof of RST Safety: Case 2
▸If sendp(m1)  sendq(m2) then deliveri(m1)  deliveri(m2)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
114
P
Q
R
[0 1 0]
[0 0 0]
[1 2 0]
0 0 1
1 0 1
0 0 0
0 0 0
1 0 2
0 0 0
0 0 1
1 0 2
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 1
0 0 0
0 0 0
1 0 1
0 0 0
0 0 0
1 0 1
0 0 0

115. Proof of RST Liveness
▸Liveness:
▹a message will never be indefinitely delayed
▹Every message will be delivered eventually
▸Must prove
▹If sendi(m) and receivej(m) then deliverj(m)
▹Counterexample:
▸∃k such that tm[k, j] will always be greater than DELIVj[k]
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
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116. Proof of RST Liveness: Counterexample
▸∃k such that tm[k, j] will always be greater than
DELIVj [k]
▸tm[k, j] is greater than DELIVj [k]
▹Process k sent messages to process j prior to message m
being sent to process j
▹Process j has not received these messages yet
▸RST assumes a lossless network
▹Process j will eventually receive the messages from k
▹tm[k, j] will eventually be less than or equal to DELIVj [k]
▸Proves if sendi(m) and receivej(m) then deliverj(m)
Theoretical Foundations > Causal Delivery > Unicast-based > RST Protocol
116

117. BSS Protocol vs. RST Protocol
▸BSS Protocol
▹Pro: Requires smaller messages (vector)
▹Con: Requires more messages (broadcast)
▸RST Protocol
▹Pro: Requires fewer messages (unicast)
▹Con: Requires larger messages (matrix)
Theoretical Foundations > Causal Delivery
117

118. Quiz Question
▸Considering the BSS and RST algorithms, which
of the following is false?
▹The BSS algorithm is designed for multicast systems.
▹The RST algorithm is designed for unicast systems.
▹The BSS algorithm requires smaller messages.
▹The RST algorithm requires more messages.
Theoretical Foundations > Causal Delivery
118

119. Team Composition
▸ 5 teams with 4 (in one case 3) members
▸ All members are supposed to contributed equally in the project
▸ Good to schedule weekly meeting for discussion checking
progress
Team Introduction
119