Consider the following algorithm that provides a solution to the 2-process critical section problem.
Considering each statement to be atomic (i.e., no need to dig into low level assembly code). Specify which of the following requirements are satisfied or not by this algorithm. If it is satisfied, explain why (with line numbers). If it is not satisfied, justify with a possible scenario by using two-column table (one column per process, interleaved execution with line numbers, see slide titled “Race Condition”). No credit if there is no justification, or justification without two-column table, or two-column without line numbers.
a. (10 pts) Mutual Exclusion b. (10 pts) Progressc. (10 pts) Bounded Waiting
Note: for interleaved execution, a process can execute any number of statements before scheduler context switches to another process.Hints: (a) mutual exclusion: while one process is already in critical section, can the other process get into critical section? (b) Progress: No one is in critical section and when both are interested to get into critical section, can at least one eventually get in?
(c) Bounded waiting: process A is in critical section and process B stays outside. Is it possible that A gets out of critical section and then can re-enter critical section while B is still stuck outside of critical section?
Consider the following code example for allocating and releasing processes (i.e., tracking number of processes),
#define MAX_PROCS 1535int number_of_processes = 0;/* the implementation of fork() calls this function */ int allocate_process() {
int new_pid;if (number_of_processes == MAX_PROCS)
return -1;else {/* allocate process resources and assign the PID to new_pid */
++number_of_processes;_x000D_
return new_pid;_x000D_

1
} }
/* the implementation of exit() calls this function */ void release_process() {
/* release process resources */ –number_of_processes;
}
a. (6 pts) Identify the race condition(s).b. (7 pts) Assume you have a mutex lock named mutex with the operations acquire() and release().the above code with acquire() and release() to prevent the race condition(s). No credit if no annotated code. c. (7 pts) Without adding any additional synchronization code (i.e., no mutex), could we replace the integer variable
int number_of_processes = 0;
with the atomic integer
atomic_t number_of_processes = 0;(which implies we also replace ++number_of_processes and –number_of_processes with atomic_add() and atomic_sub(), respectively) to prevent the race condition(s)? Why or why not?
3. (20 pts) In an operating system processes can run concurrently. Sometimes we need to impose a specific order in execution of a set of processes. We represent the execution order for a set of processes using a process execution diagram. Consider the following process execution diagram. The diagram indicates that Pr1 must terminate before Pr2, Pr3 and Pr4 start execution. It also indicates that Pr4 should start after Pr2 and Pr3 terminate and Pr2 and Pr3 can run concurrently.
We can use semaphores in order to enforce the execution order. Semaphores have two operations as explained below.

P (or wait) is used to acquire a resource. It waits for semaphore to become positive, then decrements it by 1.
V (or signal) is used to release a resource. It increments the semaphore by 1, waking up the blocked processes, if any.Let the semaphores s1, s2, and s3 be created with an initial value of 0 before processes Pr1, Pr2, Pr3, and Pr4 execute. The following pseudo code uses semaphores to enforce the execution order_s1=0; s2=0; s3=0;Pr1: body; V(s1); V(s1); Pr2: P(s1); body; V(s2); Pr3: P(s1); body; V(s3); Pr4: P(s2); P(s3); body;It is obvious that a different process execution diagram may need different number of semaphores. Note we couldconsolidate s2 and s3 so that Pr3: …; V(s2) and Pr4: P(s2); P(s2)…. But we choose not to do so. That is, for each process that is followed by an immediate successor, we always create one new semaphore.Use pseudo code (which utilizes semaphores) to enforce execution order of the following process execution diagram.

Annotate

2

Your pseudo code must specify semaphore initialization followed by the code for each process P1, P2, …, P7, similar to the example. For each process that is followed by an immediate successor, create one new semaphore, i.e., do NOT reuse nor consolidate any semaphore.
4. (30 pts) The following partial code is a bounded-buffer monitor in which the buffers are embedded within the monitor (with two condition variables). Assume any condition variable cond has two methods: cond.wait() and cond.signal(). Multiple producers and multiple consumers are running in parallel. After an item is produced, a producer invokes produce(). Before consuming an item, a consumer invokes consume(). The embedded buffer is currently full (since numItems has the value MAX_ITEMS). Implement the produce() and consume() methods in C (no need to have actual .c program). You cannot modify existing code and cannot have any additional synchronization constructs.
monitor bounded_buffer {int items[MAX_ITEMS]; /* MAX_ITEMS is a constant defined elsewhere; not a circular buffer */
int numItems = MAX_ITEMS; /* # of items in the items array, 0≤numItems≤MAX_ITEMS */ condition full, empty;/* both produce() and consume() use numItems as index to access the array */void produce(int v); /* deposit the value v to the items array */
int consume(); /* remove an item from the items array, and return the value */ }

 
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