1. Process SynchronizationContinued 7.2 The Critical-Section Problem

2. Critical section • That part of the program where shared resources are accessed • When a process executes code that manipulates shared data (or resource), we say that the process is in a critical section (CS) (for that resource)

3. Each process executes at nonzero speed but no assumption on the relative speed of n processes General structure of a process: No assumptions about order of interleaved execution The central problem is to design the entry and exit sections Framework for analysis of solutions repeat entry section critical section exit section remainder section forever

4. Three Key Requirements for a Valid Solution to the Critical Section Problem • Mutual Exclusion: At any time, at most one process can be executing critical section (CS) code • Progress: If no process is in its CS and there are one or more processes that wish to enter their CS, this selection cannot be postponed indefinitely • no process in its remainder section can participate in this decision • Bounded Waiting: After a process P has made a request to enter its CS, there is a limit on the number of times that the other processes are allowed to enter their CS, before P’s request is granted • (otherwise the process could suffer from starvation)

5. Types of Solutions • No special OS mechanisms(software approach.) • algorithms whose correctness relies only on the assumption that only one process at a time can access a memory location • Hardware solutions • rely on special machine instructions for “locking” • Operating System and Programming Language solutions (e.g. Java) • provide specific functions and data structures for the programmer to use for synchronization

6. Software solutions • Consider the 2 process case first • First 2 algorithms have problems • 3rd algorithm is correct (Peterson’s algorithm) • Generalize to n processes • the Bakery Algorithm • Notation • We start with 2 processes: P0 and P1 • When presenting process Pi, Pj always denotes the other process (i != j)

7. The shared variable turn is initialized (to 0 or 1) before executing any Pi Pi’s critical section is executed iff turn = i Pi is busy waiting if Pj is in CS Faulty Algorithm 1 - Turn taking Process Pi: //i,j= 0 or 1 repeat while(turn!=i){}; CS turn:=j; RS forever

8. Process P0: repeat while(turn!=0){}; CS turn:=1; RS forever Process P1: repeat while(turn!=1){}; CS turn:=0; RS forever Faulty Algorithm 1 side-by-side view

9. Analysis • Achieves Mutual Exclusion (busy wait) • But Progress requirement is not satisfied since it requires strict alternation of CS’s. • If one process requires its CS more often than the other, it can’t get it.

10. Keep a Boolean variable for each process: flag[0] and flag[1] Pi signals that it is ready to enter its CS by: flag[i]:=true but waits until the other has finished its CS. Faulty Algorithm 2 – Ready flag Process Pi: repeat flag[i]:=true; while(flag[j]){}; CS flag[i]:=false; RS forever

11. Process P1: repeat flag[1]:=true; while(flag[0]){}; CS flag[1]:=false; RS forever Process P0: repeat flag[0]:=true; while(flag[1]){}; CS flag[0]:=false; RS forever Faulty Algorithm 2 side-by-side view

12. Analysis • Mutual Exclusion is satisfied but not the progress requirement • For the (interleaved) sequence: • flag[0]:=true • flag[1]:=true • Both processes will wait forever

13. Initialization: flag[0]:=flag[1]:=false turn:= 0 or 1 Wish to enter CS specified by flag[i]:=true Even if both flags go up, and no matter how the instructions are interleaved, ..turn will always end up as either 0 or 1 Algorithm 3 (Peterson’s Algorithm) Process Pi: repeat flag[i]:=true; // I want in turn:=j; // but you can go first! while(flag[j]&& turn==j); CS flag[i]:=false; // I’m done RS forever

14. Peterson’s Algorithm Process P0: repeat flag[0]:=true; // 0 wants in turn:= 1; // 0 gives a chance to 1 while (flag[1]&turn=1); CS flag[0]:=false; // 0 is done RS forever Process P1: repeat flag[1]:=true; // 1 wants in turn:=0; // 1 gives a chance to 0 while (flag[0]&turn=0); CS flag[1]:=false; // 1 is done RS forever Peterson’s algorithm side-by-side view

15. Peterson’s Algorithm: Proof of Correctness • Mutual exclusion holds since: • For both P0 and P1 to be in their CS • both flag[0] and flag[1] must be true and: • turn=0 and turn=1 (at same time): impossible

16. Proof (“progress”) • Progress requirement: • Pi can be kept out of CS only if stuck in while loop • flag[j] = true and turn = j. • If Pj not ready to enter CS then flag[j] = false • Pi can then enter its CS • If Pj has set flag[j], it is also in its while loop, then either Pi or Pj will go depending on value of turn • Therefore the progress condition is met

17. Proof (“Bounded Waiting”) Process Pi: repeat flag[i]:=true; // I want in turn:=j; // but you can go first! while(flag[j]&& turn==j) ; //(loop) CS flag[i]:=false; // I’m done RS forever • Suppose Pj gets to go this time • Can it go a second time without letting Pi go? • If Pj enters CS , then turn=j • but will then reset flag[ j]=false on exit: • allowing Pi to enter CS • What if Pj tries again, and has time to reset flag[ j]=true before Pi gets to its CS? • It must also set turn=i • since Pi is (stuck) past the point where it sets turn= j: • Pi will get to enter CS • after at most one CS entry by Pj

18. What About Process Failures? • If all 3 criteria are satisfied, a valid solution will be robust for failure of a process in its remainder section (RS) since failure in RS is just like having an infinitely long RS. • However, no valid solution can provide robustness against a process failing in its critical section (CS). • Therefore a process Pi that fails in its CS must signal this fact to other processes.

19. N-Process Solution: Bakery Algorithm • “Take a number for better service...” • Before entering the CS, each Pi takes a number. • Holder of smallest number enters CS next • ..but more than one process can get the same number • If Pi and Pj receive same number: • lowest numbered process is served first • Process resets its number to 0 in the exit section • Notation: • (a,b) < (c,d) if a < c or if a = c and b < d • max(a0,...ak) is a number b such that: b >= ai for i=0,..k

20. Bakery Algorithm • Shared data: • choosing: array[0..n-1] of boolean; • initialized to false • number: array[0..n-1] of integer; • initialized to 0

21. Bakery Algorithm Process Pi: repeat choosing[i]:=true; number[i]:=max(number[0]..number[n-1])+1; choosing[i]:=false; for j:=0 to n-1 do { while (choosing[j]); while (number[j]!=0 and (number[j],j)<(number[i],i)); } CS number[i]:=0; RS forever