3. Consider a solution to thefollowing variant of the dining-philosophers proble
ID: 3617071 • Letter: 3
Question
3. Consider a solution to thefollowing variant of the dining-philosophers problem.There
are n2processes and 2n2copies of a resource. A process needs anexclusive access to
arbitrary 4 among the copies tobe able to use the resource. Processes are logically
arranged in a two dimensionaltorus: each has coordinate <i;j>, where 0 i; j n-1.
Two processes<i1;j1> and<i2;j2> are neighbors in thetorus if either i1= i2and
0 i n-1, all the processes<i; j> where 0 j n-1 operate as a table ofdining
philosophers. Similarly, for each xed0 j n - 1, all the processes<i; j>,where
0 i n-1 operate as a table of diningphilosophers. Each process belongs to two
tables, andcan obtain two copies of the resource from eachtable.
(a) Doesthis solution provide safety?
(b) If youbelieve this to be the case, then does it preventdeadlock?
(c) If youbelieve that both questions above are answered in the armative,then
does it provide lockoutfreedom?
Explanation / Answer
(a)
Yes it provides safety, by using logical as base of DiningPhilosophers problem. One Philosopher owned by each resource at atime.
(b)
If there are n2 processesand 2n2 copies of a resource.
If n=1 then 2 processes
n=2 then 4 processes
1 (0,0)
2 (0,1)
3 (1,0)
4 (1,1)
A process needs an exclusive access to arbitrary 4 amongthe copies to be able to use the resource.
Your 4 processor tablesare
States
Hypothetical
i=0
12
1 Possesses both resources
i=1
34
4 Possesses both resources
j=0
13
3 Possesses both resources
j=1
24
2 Possesses both resources
In this hypothetical situation, you have adeadlock.
States
Hypothetical
i=0
12
1 Possesses both resources
i=1
34
4 Possesses both resources
j=0
13
3 Possesses both resources
j=1
24
2 Possesses both resources
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