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SS 2014 11.06.2014 Exercises to the lecture

Concurrency Theory Sheet 8

Roland Meyer, Viktor Vafeiadis Delivery until 17.06.2014 at 12h Exercise 8.1

A data race is defined by the following predicate:

race(a, b) ⇔ (type (a) = NA ∨ type (b) = NA)

∧ (write(a) ∨ write(b))

∧ loc(a) = loc(b)

∧ ¬hb(a, b) ∧ ¬hb(b, a)

∧ a 6= b

A program is called data race free if no valid execution contains a data race.

Now consider the following program:

x = y = 0 X

NA

= 1

Y

REL

= 1

if (Y

ACQ

== 1) print(X

NA

) a) Prove or disprove that the program is data race free.

b) Change the Y

REL

= 1 command to Y

RLX

= 1. Is the program now data race free?

Exercise 8.2

Consider the following program:

a = x = y = 0 if (X

ACQ

== 1)

Y

REL

= 1

if (Y

RLX

== 1) if (a

NA

== 1)

X

RLX

= 1

a

NA

= 1

Prove or disprove that this program is data race free.

Exercise 8.3

Prove the lemma from the lecture:

consistent

TSO

(A, lab, po, rf , mo

TSO

) ⇒ ∃mo : consistent

Rel−Acq

(A, lab, po, rf , mo)

Delivery until 17.06.2014 at 12h into the box next to 34-401.4

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