While reading Sipser’s book on theory of computation, it relies heavily on the concept of formal language, and machines that merely accept or reject an input.

But most useful programs we deal with do more than merely verify an input. They compute something. We may compute a solution for an equation instead of merely verify it. We may sum a list of numbers, or calculate some function on it.

Maybe “most” is an exaggeration since I can’t prove it. But still, it begs the question. Why not deal with machines than do more than merely verify?