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What is meant by correctness of algorithm?
In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified. Best explored is functional correctness, which refers to the input-output behavior of the algorithm (i.e., for each input it produces an output satisfying the specification).
What is proof of partial correctness?
When proving that a loop (or program with a loop) is correct (with respect to some pre/post-condition pair), we prove partial correctness and termination separately. For both parts we need a loop invariant, which describes how the variables in the loop are used to achieve the postcondition.
Why is correctness of algorithm important?
Proving correctness of algorithm is crucial. For many problems, algorithms are very complex. Reliability of an algorithm cannot be claimed unless and until it gives the correct output for each of the valid inputs. Tracing the output of each possible input is impossible.
Why is correctness of Algorithm important?
How can you prove the correctness of an algorithm using loop invariant?
Termination: When the for-loop terminates i=(n−1)+1=n. Now the loop invariant gives: The variable answer contains the sum of all numbers in subarray A[0:n]=A. This is exactly the value that the algorithm should output, and which it then outputs. Therefore the algorithm is correct.
Is an algorithm a proof?
Therefore, an algorithm (which has been proven correct) is a proof.
What is partial correctness?
Partial correctness means that the program fulfills its specification, or does not terminate (infinite loop or recursion).
Why do we use literals to prove an algorithm’s correctness?
Example with literals: Because the method we are using to prove an algorithm’s correctness is math based, or rather function based, the more the solution is similar to a real mathematic function, the easier the proof. Why is this you may ask?
How to design a completely new algorithm?
When designing a completely new algorithm, a very thorough analysis of its correctness and efficiency is needed. The last thing you would want is your solution not being adequate for a problem it was designed to solve in the first place.
How do you prove correctness in sequential programming?
Given a pre- and post-condition, a standard way of proving correctness (of a sequential program) is to use Hoare logic, which is a set of axioms and inference rules. Starting from the post-condition, one systematically derives a proof-tree to prove the pr
What are approximate algorithms in computer programming?
Approximate Algorithms :- Proving correctness become slightly difficult. As now you have to prove that you algorithm my not be correct but worst case may not go far. However approximate algorithms use an underlying greedy , LP (Linear Programming) or Dynamic Programming.