Peterson’s Solution is a classical software based solution to the critical section problem

The algorithm uses two variables, flag, and turn. A flag[n] value of true indicates that the process n wants to enter the critical section. Entrance to the critical section is granted for process P0 if P1 does not want to enter its critical section or if P1 has given priority to P0 by setting turn to 0.

Peterson's Algorithm

bool flag[0] = {false}; 

bool flag[1] = {false}; 

int turn; 

P0: flag[0] = true; 

P0_gate: turn = 1; 

while (flag[1] == true && turn == 1) {

 // busy wait 

} 

// critical section ...

 // end of critical section 

flag[0] = false; 

P1: flag[1] = true; 

P1_gate: turn = 0; 

while (flag[0] == true && turn == 0) { 

// busy wait 

}

 // critical section ... 

// end of critical section 

flag[1] = false; 

The algorithm satisfies the three essential criteria to solve the critical section problem, provided that changes to the variables turn, flag[0], and flag[1] propagate immediately and atomically. The while condition works even with preemption.

The three criteria are mutual exclusion, progress, and bounded waiting.

Since turn can take on one of two values, it can be replaced by a single bit, meaning that the algorithm requires only three bits of memory.

Mutual exclusion

P0 and P1 can never be in the critical section at the same time: If P0 is in its critical section, then flag[0] is true. 

In addition, either flag[1] is false (meaning P1 has left its critical section), or turn is 0 (meaning P1 is just now trying to enter the critical section, but graciously waiting), or P1 is at label P1_gate (trying to enter its critical section, after setting flag[1] to true but before setting turn to 0 and busy waiting). 

So if both processes are in their critical sections then we conclude that the state must satisfy flag[0]and flag[1] and turn = 0 and turn = 1. 

No state can satisfy both turn = 0 and turn = 1 so there can be no state where both processes are in their critical sections. (This recounts an argument that is made rigorous in.

Progress

Progress is defined as the following: if no process is executing in its critical section and some processes wish to enter their critical sections, then only those processes that are not executing in their remainder sections can participate in making the decision as to which process will enter its critical section next. 

This selection cannot be postponed indefinitely. A process cannot immediately re-enter the critical section if the other process has set its flag to say that it would like to enter its critical section.

Bounded waiting

Bounded waiting or bounded bypass means that the number of times a process is bypassed by another process after it has indicated its desire to enter the critical section is bounded by a function of the number of processes in the system. 

In Peterson's algorithm, a process will never wait longer than one turn for entrance to the critical section: After giving priority to the other process, this process will run to completion and set its flag to 1, thereby never allowing the other process to enter the critical section.