34 The Complexity of Theorem-Proving Procedures (1971)

While discussing maximal matchings in graphs a decade after Kruskal's unelaborated claim that his spanning tree algorithm was "practical" (chapter 17), the computer scientist Jack Edmonds paused to draw the distinction between polynomial- and exponential-time algorithms (as we now call them). A "digression" near the beginning of Edmonds (1965) states, "An explanation is due on the use of the words ‘efficient algorithm.’ … For practical purposes the difference between algebraic and exponential order is often more crucial than the difference between finite and non-finite." At about the same time, the mathematician Alan Cobham (1965) formulated a machine-model-independent class he called L, the functions computable in time "bounded by polynomials in the lengths of the numbers involved" represented in digital form.