Non- Deterministic Algorithms

1. Non-Deterministic
Algorithms
Name: Dipankar Boruah
Roll no: MCA/21/24

2. Content:
 Introduction
 Deterministic algorithm
 Non-deterministic algorithm
 Stages of Non-deterministic algorithm
 Non-deterministic Search Algorithm
 Non-deterministic Sorting Algorithm
 Functions used in the Algorithm

3. Introduction
 Two types of algorithm: Deterministic and Non-deterministic.
 An algorithm which provides different output for same input is a non-
deterministic algorithm.

4. Deterministic Algorithm:
 Particular input will always produce the same output.
 Purely determines its input where no randomness is involve.
 It is uniquely defined without any ambiguity.
 Has predefined output.
q0
q1
q2
0
1
Fig:1

5. Non-deterministic Algorithm
 May not have unique results.
 There can be specific set of possibilities for each operation.
 It is a two stage algorithm (Guessing and Verification).
 No particular rule is followed here to make the guess.
q0
q1
q2
q3
0
0
0
Fig:2

6. Stages of Non-deterministic algorithm
 Non-deterministic Stage or guessing stage.
 Deterministic Stage or verification stage.

7. Non-deterministic Stage(Guessing stage)
 Here it generate an arbitrary string that can be thought of as a candidate
solution.

8. Deterministic Stage(Verification stage)
 In this stage we take candidate solution and instance of the problem as the
input.
 It returns yes if the candidate represent the actual solution(if the guessing is
correct).
 If the answer is no our guessing is wrong.

9. Non-deterministic Algorithm
 A Non-deterministic Algorithm terminates if and only if there exist no set of
choices leading to a successful signal.
 A machine that is capable of executing a Non-deterministic Algorithm is called
as Non-deterministic machine, Non-deterministic finite automata(NFA).

10. Non-deterministic Search Algorithm
No looping so, complexity = O(1)
Searching x on A[1:n], on success returns j if A[j]=x or return 0 otherwise
j = choice(1,n); //j will return a arbitrary value form 1 to n
if (A[j]==x) then {write(j); success();} /*if we find the search item x in jth location
then write() will write the value of j in
output and success() will indicate
successful completion.*/
write(0); Failure(); //will indicate failure

11. Non-deterministic Sorting Algorithm
No nested loops so, complexity = O(n)
Sorting array A[1:n] of positive integers in ascending order
Algorithm Nsort(A,n) //sort n positive integers.
{
for i =1 to n do B[i]=0; //Initialize B[] with all location 0
for i = 1 to n do //Searching in the main array
{
j = choice(1,n); //j will return a value form 1 to n
if(B[j]!=0)then failure();
B[j] = A[i]; //Taking a value from A[i] and putting it in B[j]th location
}
for i=1 to (n-1)do //verify order
if (B[i]>B[i+1]) then failure(); //if the items are not in ascending order will fail
write(B[1:n]); //will print the sorted array
success(); //indicate successful termination.
}

12. Functions used in the Algorithm
 Choice(s)- it randomly chooses one of the elements of set(s)
 Failure()- it signals an unsuccessful completion.
 Success()- it signals a successful completion.

13. Uses
 In a Np-problem the algorithm having non-polynomial time complexity, by
applying non-deterministic algorithm on them, the complexity might get
reduce and it can come to polynomial time.

14. Reference:
 https://www.techopedia.com/definition/18830/deterministic-algorithm
 https://www.geeksforgeeks.org/difference-between-deterministic-and-non-
deterministic-algorithms
 https://en.wikipedia.org/wiki/Nondeterministic_algorithm
 https://www.youtube.com/watch?v=ZNe1ziMExGg
 https://www.tutorialspoint.com/difference-between-deterministic-and-non-
deterministic-algorithms

15. THANK YOU