Dekker’s algorithm in Process Synchronization
Prerequisite – Process Synchronization, Inter Process Communication
To obtain such a mutual exclusion, bounded waiting, and progress there have been several algorithms implemented, one of which is Dekker’s Algorithm. To understand the algorithm let’s understand the solution to the critical section problem first.
A process is generally represented as :
do { //entry section critical section //exit section remainder section } while (TRUE);
The solution to the critical section problem must ensure the following three conditions:
- Mutual Exclusion
- Progress
- Bounded Waiting
One of the solutions for ensuring above all factors is Peterson’s solution.
Another one is Dekker’s Solution. Dekker’s algorithm was the first probably-correct solution to the critical section problem. It allows two threads to share a single-use resource without conflict, using only shared memory for communication. It avoids the strict alternation of a naĂŻve turn-taking algorithm, and was one of the first mutual exclusion algorithms to be invented.
Although there are many versions of Dekker’s Solution, the final or 5th version is the one that satisfies all of the above conditions and is the most efficient of them all.
Note – Dekker’s Solution, mentioned here, ensures mutual exclusion between two processes only, it could be extended to more than two processes with the proper use of arrays and variables.
Algorithm – It requires both an array of Boolean values and an integer variable:
var flag: array [0..1] of boolean; turn: 0..1; repeat flag[i] := true; while flag[j] do if turn = j then begin flag[i] := false; while turn = j do no-op; flag[i] := true; end; critical section turn := j; flag[i] := false; remainder section until false;
First Version of Dekker’s Solution – The idea is to use a common or shared thread number between processes and stop the other process from entering its critical section if the shared thread indicates the former one already running.
CPP
Main() { int thread_number = 1; startThreads(); } Thread1() { do { // entry section // wait until threadnumber is 1 while (threadnumber == 2) ; // critical section // exit section // give access to the other thread threadnumber = 2; // remainder section } while (completed == false ) } Thread2() { do { // entry section // wait until threadnumber is 2 while (threadnumber == 1) ; // critical section // exit section // give access to the other thread threadnumber = 1; // remainder section } while (completed == false ) } |
Python3
def Thread1(): doWhile = False while not completed or not doWhile: doWhile = True # entry section # wait until threadnumber is 1 while (threadnumber = = 2 ): pass # critical section # exit section # give access to the other thread threadnumber = 2 # remainder section def Thread2(): doWhile = False while not completed or not doWhile: doWhile = True # entry section # wait until threadnumber is 2 while (threadnumber = = 1 ): pass # critical section # exit section # give access to the other thread threadnumber = 1 # remainder section if __name__ = = '__main__' : thread_number = 1 startThreads() |
The problem arising in the above implementation is lockstep synchronization, i.e each thread depends on the other for its execution. If one of the processes completes, then the second process runs, gives access to the completed one, and waits for its turn, however, the former process is already completed and would never run to return the access back to the latter one. Hence, the second process waits infinitely then.
Second Version of Dekker’s Solution – To remove lockstep synchronization, it uses two flags to indicate its current status and updates them accordingly at the entry and exit section.
CPP
Main() { // flags to indicate if each thread is in // its critical section or not. boolean thread1 = false ; boolean thread2 = false ; startThreads(); } Thread1() { do { // entry section // wait until thread2 is in its critical section while (thread2 == true ) ; // indicate thread1 entering its critical section thread1 = true ; // critical section // exit section // indicate thread1 exiting its critical section thread1 = false ; // remainder section } while (completed == false ) } Thread2() { do { // entry section // wait until thread1 is in its critical section while (thread1 == true ) ; // indicate thread2 entering its critical section thread2 = true ; // critical section // exit section // indicate thread2 exiting its critical section thread2 = false ; // remainder section } while (completed == false ) } |
Python3
def Thread1(): doWhile = False while not completed or not doWhile: doWhile = True # entry section # wait until thread2 is in its critical section while (thread2): pass # indicate thread1 entering its critical section thread1 = True # critical section # exit section # indicate thread1 exiting its critical section thread1 = False # remainder section def Thread2(): doWhile = False while not completed or not doWhile: doWhile = True # entry section # wait until thread1 is in its critical section while (thread1): pass # indicate thread1 entering its critical section thread2 = True # critical section # exit section # indicate thread2 exiting its critical section thread2 = False # remainder section if __name__ = = '__main__' : # flags to indicate if each thread is in # its critical section or not. thread1 = False thread2 = False startThreads() |
The problem arising in the above version is mutual exclusion itself. If threads are preempted (stopped) during flag updation ( i.e during current_thread = true ) then, both the threads enter their critical section once the preempted thread is restarted, also the same can be observed at the start itself, when both the flags are false.
Third Version of Dekker’s Solution – To re-ensure mutual exclusion, it sets the flags before the entry section itself.
C++
Main() { // flags to indicate if each thread is in // queue to enter its critical section boolean thread1wantstoenter = false ; boolean thread2wantstoenter = false ; startThreads(); } Thread1() { do { thread1wantstoenter = true ; // entry section // wait until thread2 wants to enter // its critical section while (thread2wantstoenter == true ) ; // critical section // exit section // indicate thread1 has completed // its critical section thread1wantstoenter = false ; // remainder section } while (completed == false ) } Thread2() { do { thread2wantstoenter = true ; // entry section // wait until thread1 wants to enter // its critical section while (thread1wantstoenter == true ) ; // critical section // exit section // indicate thread2 has completed // its critical section thread2wantstoenter = false ; // remainder section } while (completed == false ) } |
Python3
if __name__ = = '__main__' : # flags to indicate if each thread is in # queue to enter its critical section thread1wantstoenter = False thread2wantstoenter = False startThreads() def Thread1(): doWhile = False while (completed = = False or not doWhile): doWhile = True thread1wantstoenter = True # entry section # wait until thread2 wants to enter # its critical section while (thread2wantstoenter = = True ): pass # critical section # exit section # indicate thread1 has completed # its critical section thread1wantstoenter = False # remainder section def Thread2(): doWhile = False while (completed = = False or not doWhile) : doWhile = True thread2wantstoenter = True # entry section # wait until thread1 wants to enter # its critical section while (thread1wantstoenter = = True ): pass # critical section # exit section # indicate thread2 has completed # its critical section thread2wantstoenter = False # remainder section |
The problem with this version is a deadlock possibility. Both threads could set their flag as true simultaneously and both will wait infinitely later on.
Fourth Version of Dekker’s Solution – Uses small time interval to recheck the condition, eliminates deadlock, and ensures mutual exclusion as well.
CPP
Main() { // flags to indicate if each thread is in // queue to enter its critical section boolean thread1wantstoenter = false ; boolean thread2wantstoenter = false ; startThreads(); } Thread1() { do { thread1wantstoenter = true ; while (thread2wantstoenter == true ) { // gives access to other thread // wait for random amount of time thread1wantstoenter = false ; thread1wantstoenter = true ; } // entry section // wait until thread2 wants to enter // its critical section // critical section // exit section // indicate thread1 has completed // its critical section thread1wantstoenter = false ; // remainder section } while (completed == false ) } Thread2() { do { thread2wantstoenter = true ; while (thread1wantstoenter == true ) { // gives access to other thread // wait for random amount of time thread2wantstoenter = false ; thread2wantstoenter = true ; } // entry section // wait until thread1 wants to enter // its critical section // critical section // exit section // indicate thread2 has completed // its critical section thread2wantstoenter = false ; // remainder section } while (completed == false ) } |
Python3
if __name__ = = '__main__' : # flags to indicate if each thread is in # queue to enter its critical section thread1wantstoenter = False thread2wantstoenter = False startThreads() def Thread1(): doWhile = False while (completed = = False or not doWhile): doWhile = True thread1wantstoenter = True while (thread2wantstoenter = = True ) : # gives access to other thread # wait for random amount of time thread1wantstoenter = False thread1wantstoenter = True # entry section # wait until thread2 wants to enter # its critical section # critical section # exit section # indicate thread1 has completed # its critical section thread1wantstoenter = False # remainder section def Thread2(): doWhile = False while (completed = = False or not doWhile): doWhile = True thread2wantstoenter = True while (thread1wantstoenter = = True ) : # gives access to other thread # wait for random amount of time thread2wantstoenter = False thread2wantstoenter = True # entry section # wait until thread1 wants to enter # its critical section # critical section # exit section # indicate thread2 has completed # its critical section thread2wantstoenter = False # remainder section |
The problem with this version is the indefinite postponement. Also, a random amount of time is erratic depending upon the situation in which the algorithm is being implemented, hence not an acceptable solution in business critical systems.
Dekker’s Algorithm: Final and completed Solution – -Idea is to use favoured thread notion to determine entry to the critical section. Favoured thread alternates between the thread providing mutual exclusion and avoiding deadlock, indefinite postponement, or lockstep synchronization.
CPP
Main() { // to denote which thread will enter next int favouredthread = 1; // flags to indicate if each thread is in // queue to enter its critical section boolean thread1wantstoenter = false ; boolean thread2wantstoenter = false ; startThreads(); } Thread1() { do { thread1wantstoenter = true ; // entry section // wait until thread2 wants to enter // its critical section while (thread2wantstoenter == true ) { // if 2nd thread is more favored if (favaouredthread == 2) { // gives access to other thread thread1wantstoenter = false ; // wait until this thread is favored while (favouredthread == 2) ; thread1wantstoenter = true ; } } // critical section // favor the 2nd thread favouredthread = 2; // exit section // indicate thread1 has completed // its critical section thread1wantstoenter = false ; // remainder section } while (completed == false ) } Thread2() { do { thread2wantstoenter = true ; // entry section // wait until thread1 wants to enter // its critical section while (thread1wantstoenter == true ) { // if 1st thread is more favored if (favaouredthread == 1) { // gives access to other thread thread2wantstoenter = false ; // wait until this thread is favored while (favouredthread == 1) ; thread2wantstoenter = true ; } } // critical section // favour the 1st thread favouredthread = 1; // exit section // indicate thread2 has completed // its critical section thread2wantstoenter = false ; // remainder section } while (completed == false ) } |
Python3
if __name__ = = '__main__' : # to denote which thread will enter next favouredthread = 1 # flags to indicate if each thread is in # queue to enter its critical section thread1wantstoenter = False thread2wantstoenter = False startThreads() def Thread1(): doWhile = False while (completed = = False or not doWhile) : doWhile = True thread1wantstoenter = True # entry section # wait until thread2 wants to enter # its critical section while (thread2wantstoenter = = True ) : # if 2nd thread is more favored if (favaouredthread = = 2 ) : # gives access to other thread thread1wantstoenter = False # wait until this thread is favored while (favouredthread = = 2 ): pass thread1wantstoenter = True # critical section # favor the 2nd thread favouredthread = 2 # exit section # indicate thread1 has completed # its critical section thread1wantstoenter = False # remainder section def Thread2(): doWhile = False while (completed = = False or not doWhile) : doWhile = True thread2wantstoenter = True # entry section # wait until thread1 wants to enter # its critical section while (thread1wantstoenter = = True ) : # if 1st thread is more favored if (favaouredthread = = 1 ) : # gives access to other thread thread2wantstoenter = False # wait until this thread is favored while (favouredthread = = 1 ): pass thread2wantstoenter = True # critical section # favour the 1st thread favouredthread = 1 # exit section # indicate thread2 has completed # its critical section thread2wantstoenter = False # remainder section |
This version guarantees a complete solution to the critical solution problem.
References –
Dekker’s Algorithm -csisdmz.ul.ie
Dekker’s algorithm – Wikipedia