Nonclassical computation-a dynamical systems perspective

Abstract

In this chapter, computation is investigated from a dynamical systems perspective. A dynamical system is described in terms of its abstract state space, the system's current state within its state space, and a rule that determines its motion through its state space. In a classical computational system, that rule is given explicitly by the computer program; in a physical system, that rule is the underlying physical law governing the behavior of the system. Therefore, a dynamical systems approach to computation allows one to take a unified view of computation in classical discrete systems and in systems performing nonclassical computation. In particular, it gives a route to a computational interpretation of physical embodied systems exploiting the natural dynamics of their material substrates.