1,009 views
1 votes
1 votes

Let there be ‘m’ resources of single instance & ‘n’ processes. ‘A’ represents sum of allocation matrix for all processes, ‘N’ represents sum of need matrix and ‘M’ represents sum of max matrix for all processes. The conditions for which system is dead lock free is

  1.   0≤N≤m and M≤m+n
  2.   1<A<m and M≤m+n
  3.   1≤N≤m and M<m+n

1 Answer

0 votes
0 votes
1≤N≤m and M<m+n
Proof by contradiction
Assume deadlock is present: then A=M because there is only one type of resource and resources are acquired & released one at a time.
We know that M=N+A (MAX=NEED+ALLOCATION) from second condition (M<m+n),
M<m+n
N+A<m+n
N+M<m+n (from step1)
=N<n
It means at least one process need=0, means that n-1 process shares ‘m’ resources which contradicts the statement. Hence deadlock is not present.

Related questions

1 votes
1 votes
4 answers
1
Purple asked Jan 29, 2016
7,702 views
Which of the following is not a necessary condition for a deadlock among processes?(a) Shared Resources(b) No Preemption(c) Acyclic condition among processes(d) None of t...
0 votes
0 votes
1 answer
2
1 votes
1 votes
1 answer
3
Umang Raman asked Oct 19, 2015
2,035 views
Which of the following is not a necessary condition(s) for a deadlock?1.Mutual Exclusion2.Hold and wait3.No pre-emption4.Re-entrancy
2 votes
2 votes
4 answers
4
ajit asked Sep 17, 2015
39,457 views
which of the following is not a necessary condition for deadlock?a)Mutual exclusionb)Reentrancyc)Hold and Waitd)No pre-emption