Cobham's Thesis

Cobham's thesis, also known as Cobham–Edmonds thesis (named after Alan Cobham and Jack Edmonds), asserts that computational problems can be feasibly computed on some computational device only if they can be computed in polynomial time; that is, if they lie in the complexity class P.

Formally, to say that a problem can be solved in polynomial time is to say that there exists an algorithm that, given an n-bit instance of the problem as input, can produce a solution in time O(nc), where c is a constant that depends on the problem but not the particular instance of the problem.

Alan Cobham's 1965 paper entitled "The intrinsic computational difficulty of functions" is one of the earliest mentions of the concept of the complexity class P, consisting of problems decidable in polynomial time. Cobham theorized that this complexity class was a good way to describe the set of feasibly computable problems. Any problem that cannot be contained in P is not feasible, but if a real-world problem can be solved by an algorithm existing in P, generally such an algorithm will eventually be discovered.

The class P is a useful object of study because it is not sensitive to the details of the model of computation: for example, a change from a single-tape Turing machine to a multi-tape machine can lead to a quadratic speedup, but any algorithm that runs in polynomial time under one model also does so on the other.

In similar spirit, NC complexity class can be thought to capture problems "effectively solvable" on a parallel computer.