Difference between Deterministic and Non-deterministic Algorithms

In a deterministic algorithm, for a given particular input, the computer will always produce the same output going through the same states but in the case of the non-deterministic algorithm, for the same input, the compiler may produce different output in different runs. In fact, non-deterministic algorithms can’t solve the problem in polynomial time and can’t determine what is the next step. The non-deterministic algorithms can show different behaviors for the same input on different execution and there is a degree of randomness to it.

To implement a non-deterministic algorithm, we have a couple of languages like Prolog but these don’t have standard programming language operators and these operators are not a part of any standard programming languages. Some of the terms related to the non-deterministic algorithm are defined below:

• choice(X): chooses any value randomly from the set X.
• failure(): denotes the unsuccessful solution.
• success(): The solution is successful and the current thread terminates.

Example :

Problem Statement : Search an element x on A[1:n] where n>=1, on successful search return j if a[j] is equals to x otherwise return 0. Non-deterministic Algorithm for this problem :

1.j= choice(a, n)
2.if(A[j]==x) then
    {
       write(j);
       success();
    }
3.write(0); failure();

Deterministic Algorithm	Non-deterministic Algorithm
For a particular input, the computer will give always the same output.	For a particular input the computer will give different outputs on different execution.
Can solve the problem in polynomial time.	Can’t solve the problem in polynomial time.
Can determine the next step of execution.	Cannot determine the next step of execution due to more than one path the algorithm can take.

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