I propose to investigate the problem of empirical equivalence by performing numerical calculations, simulating hypothetical physical systems, with known evolution rules, which include a robot performing an experiment. The aim of the experiments of the robot is to discover the rules governing the system in which it is simulated. The proposed numerical calculation is actually a thought experiment: I discuss the principles of how the discussion on the empirical equivalence should be performed; the discussion is based on the evaluation of (...) the complexity classes of problems connected to the numerical calculation. Based on this discussion, I prove a sufficient condition for empirical equivalence, which is based on the existence of a transformation belonging to a given complexity class. (shrink)