Artificial Intelligence Programming 2025 – 400 Free Practice Questions to Pass the Exam

NP-Complete problems are indeed characterized by their verifiability in polynomial time. This means that if you have a proposed solution (or certificate) for an NP-Complete problem, it can be checked to see if it's valid relative to the input in a time that is bounded by a polynomial function of the size of the input.

To clarify further, given a solution to a problem in NP, you can run a verification algorithm that will check the solution's correctness efficiently. This efficiency is crucial as it allows NP-Complete problems to be manageable in terms of checking potential solutions, despite the fact that finding a solution might take longer or be computationally intensive.

For example, problems like the Traveling Salesman Problem can be hard to solve (exponential time complexity) but if someone gives you a route, you can quickly compute the total distance to verify if it's the shortest path among a set of cities, which takes polynomial time relative to the number of cities.

In contrast, linear time would suggest an even faster verification process, which is not always the case for NP-Complete problems, and exponential time would imply that the verification process becomes impractically long as problem sizes grow. Constant time verification is not viable for NP-Complete problems as it