One way to eliminate circular wait is to have rule saying that a process is entitled only to a single resource at any moment. Give an example to show that this restriction is unacceptable in many cases.

A system has four processes and five allocatable resources. The current allocation and maximum needs are as follows: What is the smallest value of x for which this is a safe state?

The banker’s algorithm is being run in a system with $m$ resource classes and $n$ processes. In the limit of large $m$ and $n,$ the number of operations that must be performed to check a state for safety is proportional to $m^{a} n^{b}.$ What are the values of $a$ and $b?$

Consider the previous problem again, but now with $p$ processes each needing a maximum of $m$ resources and a total of $r$ resources available. What condition must hold to make the system deadlock free?