David Chalmers has defended an account of what it is for a physical system to implement a computation. The account appeals to the idea of a “combinatorial-state automaton” or CSA. It is not entirely clear whether Chalmers intends the CSA to be a full-blown computational model, or merely a convenient formalism into which instances of other models can be translated. I argue that the CSA is not a computational model in the usual sense because CSAs do not perspicuously represent algorithms, and because they are too powerful both in that they can perform any computation in a single step and in that without so far unspecified restrictions they can “compute” the uncomputable. In addition, I suggest that finite, inputless CSAs have trivial implementations very similar to those they were introduced to avoid.
Curtis Brown, “Combinatorial-State Automata and Models of Computation,” Journal of Cognitive Science 13 (2012): 51-73.
Journal of Cognitive Science