Dynamic systems and analog computation

The term analog computation evokes numerous associations; the planimeter, the slide rule, the differential analyzer, and other physical computing devices are modeled by mathematical equations with diverse applications. By drawing a careful distinction between analog and digital computation, it becomes possible to compare the use of analog computation in the solution of various optimization problems with the use of digital computation. The famous open question of complexity theory for digital computation, whether or not P = NP, owes its practical importance to the ability of the Turing machine model for digital computation to provide a realistic, ideal model for a digital computer. It being widely assumed that P ?? NP, NP-complete decision problems are widely regarded as intractable. (Here we remind the reader that this kind of complexity analysis deals with worst case analysis of infinite families of combinatorial optimization problems, and intractability refers to asymptotic rate of growth of computational requirements for larger and larger problem instances. For further reference, see [GJ].)