This is the third in a series of three papers devoted to energy flow and entropy changes in chemical and biological processes, and their relations to the thermodynamics of computation. The previous two papers have developed reversible chemical transformations as idealizations for studying physiology and natural selection, and derived bounds from the second law of thermodynamics, between information gain in an ensemble and the chemical work required to produce it. This paper concerns the explicit mapping of chemistry to computation, and particularly the Landauer decomposition of irreversible computations, in which reversible logical operations generating no heat are separated from heat-generating erasure steps which are logically irreversible but thermodynamically reversible. The Landauer arrangement of computation is shown to produce the same entropy-flow diagram as that of the chemical Carnot cycles used in the second paper of the series to idealize physiological cycles. The specific application of computation to data compression and error-correcting encoding also makes possible a Landauer analysis of the somewhat different problem of optimal molecular recognition, which has been considered as an information theory problem. It is shown here that bounds on maximum sequence discrimination from the enthalpy of complex formation, although derived from the same logical model as the Shannon theorem for channel capacity, arise from exactly the opposite model for erasure.