1. path {open + read}; close end

   The expression allows several open or read followed by a close. Only open or only read can be executed at a given time.

2. path {openread ; read} ; {openwrite ; write} end

   It allows an openread followed by a read; several of these can occur at the same time. These are then be followed by the execution of several of "an openwrite followed by a write".

P₁ → R₁, P₂ → R₂, P₃ → R₂, P₄ → R₂, P₅ → R₃,
P₄ ← R₁, P₃ ← R₂, P₅ ← R₂, P₃ ← R₃,

Draw the graph. Give an example of a knot in the graph and explain why it is a knot. If you find that there's no knot in the graph, express the answer as an empty set.

Knot K = { R2, P5, R3, P3 }

Reasons:

1. Any node can reach any other node in the set K.
2. Any node in the set K cannot access other nodes outside K.

Max-Claim B =

2 2 2 1 2 2 3 1 3

Allocation C =

1 1 0 1 0 1 1 1 1

a) Find the available matrix D and need matrix E in this state.

Available matrix D = (2 0 2 )

Need matrix E =

1 1 2 0 2 1 2 0 2

b) Suppose now process P₁ makes a request with

Available matrix D = (2 0 1 )

Allocation matrix C =		1 1 1 1 0 1 1 1 1
Need matrix E =		1 1 1 0 2 1 2 0 2

c) To ensure the system be safe, should the request be granted? Why? Give your reasons in detail.

It should not be granted because the remaining resources ( 2 0 1 ) cannot satisfy the maximum need of any process. i.e.,

D = ( 2 0 1 )		E1 = ( 1 1 1 )
D = ( 2 0 1 )		E2 = ( 0 2 1 )
D = ( 2 0 1 )		E3 = ( 2 0 2 )

a → b iff t^a < t^b

Yes. .....

1 0 0

,

0 1 0

,

0 0 1

a) Draw a diagram to show all the transitions and events.

b) Find the vector clocks of all the events.

c) Give an example for each of the following:

i) a strongly consistent state

ii) a consistent but not strongly consistent state

iii) an inconsistent state

Solutions

a) and b)

c) Example of :

i) a strongly consistent state: {e11, e21, e31}

ii) a consistent but not strongly consistent state: {e13, e21, e31}

iii) an inconsistent state: {e14, e25, e33}