Resources on proving algorithms correct?

• BicycleTree
In summary, the conversation discusses the search for resources on proving algorithms correct. The speaker mentions their background and difficulty finding formal treatments and precise definitions of algorithms. They ask for suggestions and are recommended "The Art of Computer Programming" by Donald Knuth and "Introduction to Algorithms" by Cormen Leiserson and Rivest. The latter is deemed to be more suitable for their needs.
BicycleTree
Where can I find resources on proving algorithms correct? I'm looking for a formal treatment (hopefully I have enough background by now to absorb that). I keep seeing these proofs of algorithms and references to proofs of algorithms but everything is informal and I've never even seen a precise definition of "algorithm."

I can't find much on Google or Mathworld. Judging by the online descriptions of courses about algorithmic proof, there must be plenty of information out there, but it's not very accessible. I'd appreciate any suggestions.

"The Art of Computer Programming" by Donald Knuth.

There's also Introduction to Algorithms, Cormen Leiserson and Rivest.

Thanks. The Art of Computer Programming looks very good, but it's probably more comprehensive than I'm looking for right now. Introduction to Algorithms looks like it's exactly what I seek.

1. What is the importance of proving algorithms correct?

Proving algorithms correct is crucial because it ensures that the algorithm will produce the expected and desired result, without any errors or bugs. This is especially important in critical systems such as medical devices or transportation systems.

2. How do you prove an algorithm correct?

There are various methods for proving algorithms correct, such as mathematical induction, loop invariants, and program verification. These methods involve analyzing the algorithm's logic and structure to ensure that it will always produce the correct output for all possible inputs.

3. Can an algorithm be proven correct in all cases?

No, it is not always possible to prove an algorithm correct in all cases. Some algorithms may have complex logic or rely on external factors that make it difficult to prove their correctness. However, thorough testing and verification can increase confidence in an algorithm's correctness.

4. What are some common mistakes to avoid when proving algorithms correct?

Some common mistakes to avoid when proving algorithms correct include overlooking edge cases, assuming the algorithm will always terminate, and not considering all possible inputs. It is important to be thorough and rigorous in the analysis and verification process.

5. Are there any resources available for learning how to prove algorithms correct?

Yes, there are many resources available for learning how to prove algorithms correct, including textbooks, online courses, and tutorials. Additionally, there are tools and software that can assist in the verification process. It is also helpful to consult with experienced colleagues or experts in the field.

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