What best describes a characteristic of NP-complete problems?

A characteristic of NP-complete problems is that they can be checked quickly once a solution is provided. NP-complete problems are a subset of NP (nondeterministic polynomial time) problems, which means that if you have a candidate solution, you can verify whether it is indeed a valid solution in polynomial time. This is a critical aspect because it highlights the distinction between finding a solution and verifying one.

In computational complexity theory, this property is essential because it implies that while we may not know how to find solutions efficiently for all NP-complete problems, once a solution is guessed or provided, validating its correctness does not require excessive computation. This verification process is typically efficient, thus allowing problems that seem difficult to solve directly to be evaluated swiftly.

The other choices suggest features that do not align with the true nature of NP-complete problems. Polynomial-time solutions are not guaranteed for NP-complete problems, and stating they are trivial misses the significant complexity they often embody. Also, verification methods for NP-complete problems are focused on efficiency, not complexity, making the characteristic of quick verification the most accurate description.