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Consider the following procedure CAS (”Compare-And-Swap”), where r = CAS(x, e, n) means that the procedure returns the final value of r.

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SS 2014 14.05.2014 Exercises to the lecture

Concurrency Theory Sheet 4

Roland Meyer, Viktor Vafeiadis Delivery until 20.05.2014 at 12h Exercise 4.1

Consider the following procedure CAS (”Compare-And-Swap”), where r = CAS(x, e, n) means that the procedure returns the final value of r.

r = CAS(x, e, n):

atomic ( r = [x]

if r = e then ([x] = n; r = 1) else(r = 0)

)

a) Complete the following rule so that it specifies the behaviour of CAS:

· · ·

r = CAS(x, e, n) sat ( P , R, G, Q ) b) Implement a lock using the procedure CAS.

Do not use ”assume”, but you can use ”if” and ”while”.

c) Prove that your lock implementation satisfies

sem stable(P, R) sem stable(Q, R) P ⇒ p 7→ − ∗ F p 7→ TID ∗ F ⇒ Q

{p 7→ 0 p 7→ TID} ⊆ G lock(p, TID) sat ( P , R, G, Q ) Exercise 4.2

Let ls(x, z) be defined as x = z ∧ emp ∨ ∃y. x 7→ y ∗ ls(y, z).

a) Prove (x 7→ y ∗ (P ∗ Q)) ⇒ ((x 7→ y ∗ P) ∗ Q) ∨ (P ∗ (x 7→ y ∗ Q)).

b) Prove ((x 7→ y) ∗ ls(k, m)) ⇒ (ls(k, x) ∗ ls(y, m)).

c) Conclude sem stable(ls(k, m), R) with

R := {x 7→ y (x 7→ z ∗ z 7→ y), (x 7→ z ∗ z 7→ y) x 7→ y}.

Exercise 4.3

Prove the soundness of the Prim rule:

`

SL

{P } c {Q} writes(c) ∩ fv(R, G) = ∅ c sat (P, R, G, Q)

Delivery until 20.05.2014 at 12h into the box next to 34-401.4

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