The Critical Section Problem

Problem Description
Informally, a critical section is a code segment that accesses shared variables and has to be executed as an atomic action. The critical section problem refers to the problem of how to ensure that at most one process is executing its critical section at a given time. Important: Critical sections in different threads are not necessarily the same code segment!

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Problem Description
Formally, the following requirements should be satisfied:
 Mutual exclusion: When a thread is executing in its critical

section, no other threads can be executing in their critical sections.

 Progress: If no thread is executing in its critical section, and

if there are some threads that wish to enter their critical sections, then one of these threads will get into the critical section.

 Bounded waiting: After a thread makes a request to enter its

critical section, there is a bound on the number of times that other threads are allowed to enter their critical sections, before the request is granted.

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Problem Description
In discussion of the critical section problem, we often assume that each thread is executing the following code. It is also assumed that (1) after a thread enters a critical section, it will eventually exit the critical section; (2) a thread may terminate in the non-critical section. while (true) { entry section critical section exit section non-critical section }

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Solution 1
In this solution, lock is a global variable initialized to false. A thread sets lock to true to indicate that it is entering the critical section. boolean lock = false; T0: while (true) { while (lock) { ; } lock = true; critical section lock = false; non-critical section } T1: while (true) { while (lock) { ; } lock = true; critical section lock = false; non-critical section }

(1) (2) (3) (4) (5)

(1) (2) (3) (4) (5)

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Solution 1 is incorrect!
T0
(1) context switch (1) (2) (3) context switch (2) (3) lock is set to true T0 enters the critical section T1 exits the while loop lock is set to true T1 enters the critical section

T1

Comments
T0 exits the while loop

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Solution 2
The threads use a global array intendToEnter to indicate their intention to enter the critical section. boolean intendToEnter[] = {false, false}; T0: while (true) { while (intendToEnter[1]) { ; } intendToEnter[0] = true; critical section intendToEnter[0] = false; non-critical section } T1: while (true) { while (intendToEnter[0]) { ; } intendToEnter[1] = true; critical section intendToEnter[1] = false; non-critical section }

(1) (2) (3) (4) (5)

(1) (2) (3) (4) (5)

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Solution 2 is incorrect!
T0
(1) context switch (1) (2) (3) context switch (2) (3) T1 exits the while loop intendtoEnter[1] is set to true T1 enters the critical section

T1

Comments
T0 exits the while loop

intendToEnter[0] is set to true T0 enters the critical section

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Solution 3
The global variable turn is used to indicate the next process to enter the critical section. The initial value of turn can be 0 or 1. int turn = 1; T0: while (true) { while (turn != 0) { ; } critical section turn = 1; non-critical section } T1: while (true) { while (turn != 1) { ; } critical section turn = 0; non-critical section }

(1) (2) (3) (4)

(1) (2) (3) (4)

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Solution 3 is incorrect!
T0 T1
(1) (2) (3) (4)

Comments
T1 exits the while loop T1 enters the critical section turn is set to 0 T1 terminates in non-critical section T0 exits the while loop T0 enters the critical section turn is set to 1 T0 executes non-critical section T0 repeats (1) forever

context switch (1) (2) (3) (4) (1)

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Solution 4
When a thread finds that the other thread also intends to enter its critical section, it sets its own intendToEnter flag to false and waits until the other thread exits its critical section. boolean intendToEnter[] = {false, false}; T0: while (true) { intendToEnter[0] = true; while (intendToEnter[1]) { intendToEnter[0] = false; while (intendToEnter[1]) {;} intendToEnter[0] = true; } critical section intendToEnter[0] = false; non-critical section } T1: while (true) { intendToEnter[1] = true; while (intendToEnter[0]) { intendToEnter[1] = false; while (intendToEnter[0]) {;} intendToEnter[1] = true; } critical section intendToEnter[1] = false; non-critical section }

(1) (2) (3) (4) (5) (6) (7) (8)

(1) (2) (3) (4) (5) (6) (7) (8)

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Solution 4 is incorrect!
T0
(1) (2) (6) context switch (1) (2) (3) (4)

T1

Comments intendToEnter[0] is set to true T0 exits while loop T0 enters critical section; intendToEnter[0] is true intendToEnter[1] is set to true T1 enters while (intendToEnter[0]) loop intendToEnter[1] is set to false T1 enters second while(intendToEnter[0]) loop intendToEnter[0] is set to false T0 executes the non-critical section intendToEnter[0] is set to true T0 exits while loop T0 enters critical section; intendToEnter[0] is true

context switch (7) (8) (1) (2) (6)

context switch context switch (4)

T1 is still waiting for intendToEnter[0] to be false

(7) (8) (1) (2) (6)

context switch context switch (4)

intendToEnter[0] is set to false T0 executes the non-critical section intendToEnter[0] is set to true T0 exits while loop T0 enters critical section; intendToEnter[0] is true
T1 is still waiting for intendToEnter[0] to be false

repeat infinitely

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How to check a solution
Informally, we should consider three important cases:
1. One thread intends to enter its critical section,

and the other thread is not in its critical section or in its entry section.
2. One thread intends to enter its critical section,

and the other thread is in its critical section.
3. Both threads intend to enter their critical

sections.

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Peterson’s algorithm
Peterson’s algorithm is a combination of solutions (3) and (4). boolean intendToEnter[]= {false, false}; int turn; // no initial value for turn is needed. T0: while (true) { intendToEnter[0] = true; turn = 1; while (intendToEnter[1] && turn == 1) { ; } critical section intendToEnter[0] = false; non-critical section } T1: while (true) { intendToEnter[1] = true; turn = 0; while (intendToEnter[0] && turn == 0) { ; } critical section intendToEnter[1] = false; non-critical section }

(1) (2) (3) (4) (5) (6)

(1) (2) (3) (4) (5) (6)

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Peterson’s algorithm
Informally, we consider the following cases:
1. Assume that one thread, say T0, intends to enter

its critical section and T1 is not in its critical section or its entry-section. Then intendToEnter[0] is true and intendToEnter[1] is false and T0 will enter the critical section immediately.

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Peterson’s algorithm
2. Assume that thread T0 intends to enter its

critical section and T1 is in its critical section. Since turn = 1, T0 loops at statement (3). After the execution of (5) by T1, if T0 resumes execution before T1 intends to enter again, T0 enters its critical section immediately; otherwise, see case (3).

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Peterson’s algorithm
3. Assume both threads intend to enter the critical

section, i.e. both threads have set their intendToEnter flags to true. The thread that first executes “turn = ...;” waits until the other thread executes “turn = ...;” and then enters its critical section. The other thread will be the next thread to enter the critical section.

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Peterson’s algorithm
T0
(1) context switch (1) (2) (3)

T1

Comments intendToEnter[0] is set to true intendToEnter[1] is set to true turn is set to 0 T1 enters the while loop turn is set to 1 T0 enters the while loop

context switch (2) (3) context switch

context switch (3) (4) (5) (6)

(3) (4) (5) (6) (1) (2) (3)

T1 exits while loop T1 enters the critical section intendToEnter[1] is set to false T1 executes the non-critical section intendToEnter[1] is set to true turn is set to 0 T1 enters while loop T0 exits while loop T0 enters critical section intendToEnter[0] is set to false T0 executes the non-critical section

context switch (3) (4)

T1 exits the while loop T1 enters critical section

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Bakery algorithm
Bakery algorithm is used to solve the n-process critical section problem. The main idea is the following:
 When a thread wants to enter a critical section, it

gets a ticket. Each ticket has a number.

 Threads are allowed to enter the critical section in

ascending order of their ticket numbers.

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Version 1 int number[n]; // array of ticket numbers, initially all elements of number is 0 while (true) { number[i] = max(number) + 1; for (int j = 0; j < n; j ++) { while (j != i && number[j] != 0 && (number[j], j) < (number[i], i)) { ;} } critical section number[i] = 0; non-critical section } • (a, b) < (c, d) if a < c or (a == c and b < d) • max(number) is the max value of all the elements in number

(1) (2) (3) (4) (5) (6)

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Version 1 is incorrect!
T0
(1) (1) (2) (3) (4)

T1

Comments
T0 executes max(number) + 1, switch occur before 1 is assigned to number[0] T1 sets number[1] to 1 T1 starts for loop T1 exits while and for loop T1 enters critical section T0 assigns 1 (not 2) to number[0] T0 starts for loop To exits the while and for loops T0 enters critical section

context switch (1) (2) (3) (4)

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Bakery algorithm int number[n]; // array of ticket numbers, initially all elements of number is 0 boolean choosing[n]; // initially all elements of choosing is false while (true) { choosing[i] = true; number[i] = max(number) + 1; choosing[i] = false; for (int j = 0; j < n; j ++) { while (choosing[j]) { ; } while (j != i && number[j] != 0 && (number[j], j) < (number[i], i)) { ;} } critical section number[i] = 0; non-critical section } • (a, b) < (c, d) if a < c or (a == c and b < d) • max(number) is the max value of all the elements in number (1) (2) (3) (4) (5) (6) (7) (8) (9)

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Bakery algorithm
Let us consider the following cases:
1.

One thread, say Ti, intends to enter its critical section and no other thread is in its critical section or entry section. Then number[i] = 1 and number[j], where j ≠ i, is 0. Thus, Ti enters its critical section immediately. section and Tk, k ≠ i, is in its critical section. Then at (6), when j = k, number[j] < number[i]. Thus, Ti is delayed at (6) until Tk executes (8).

2. One thread, say Ti, intends to enter its critical

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Bakery algorithm
3. Two or more threads intend to enter their

critical sections and no other threads is in its critical section. Assume that Tk and Tm, where k < m, intend to enter. Consider the possible relationships between number[k] and number[m]:
  

number[k] < number[m]. Tk enters its critical section since (number[m], m) > (number[k], k). number[k] == number[m]. Tk enters its critical section since (number[m], m) > (number[k], k). number[k] > number[m]. Tm enters its critical section since (number[k], k) > (number[m], m).

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