 The basic problem that any account of concrete computation must solve can be seen via the following diagram. Consider some computational system C (e.g. an abstract automaton) and a physical system P. System C has computational states s1 and s2 such that C transitions from s1 to s2 according to the specification of C. System P has physical states p1 and p2 such that P transitions from p1 to p2 according to the dynamics of P. The transitions among states of the same type—the arrows in the diagram—are not in need of explanation: they are either stipulated in the case of C, or well-understood physical dynamics in the case of P. However, in order for P to count as an implementation of C, the putative connection between the states of one type of system and the states of the other (the dotted lines) must be explained. The following accounts offer different ways of characterizing this connection, either by making precise what the dotted lines represent, by narrowing the possible physical states or transitions that could comprise P, or both.