1. Raymond Mutual Exclusion

2. Actions <Upon request>  Request.(h.j) = Request.(h.j)  {j}
h.j = k /\ h.k = k /\ j Request.k
h.k = j, h.j = j, Request.k = Request.k – {j}

3. Actions
h.j = j 
Access critical section

4. Slight modification h.j = k /\ h.k = k /\ j Request.k /\
(P.j = k \/ P.k = j) 
h.k = j, h.j = j, Request.k = Request.k – {j}

5. Fault-Tolerant Mutual Exclusion
What happens if the tree is broken due to faults?
A tree correction algorithm could be used to fix the tree
Example: we considered one such algorithm before

6. However,
Even if the tree is fixed, the holder relation may not be accurate

7. Invariant for holder relation
What are the conditions that are always true about holder relation?

8. Invariant h.j {j, P.j}  ch.j P.j  j  (h.j = P.j \/ h.(P.j) = j)
Plus all the predicates in the invariant of the tree program

9. Recovery from faults
h.j  {j, P.j}  ch.j 
h.j = P.j

10. Recovery from faults P.j  j /\  (h.j = P.j \/ h.(P.j) = j) 

11. Recovery from Faults P.j  j /\ (h.j = P.j /\ h.(P.j) = j) 
h.(P.j) = P.(P.j)

12. Notion of Superposition