 This appears to be the case even if we restrict ourselves to weaker computational models like total functions, but more research is necessary. There seems to be no a priori mathematical justification for the approach, although two-part code optimization continues to be a valid approach in an empirical setting of data sets that have been created on the basis of repeated observations. Phenomena that might be related to a theory of structural information and that currently are ill-understood are: phase transitions in the hardness of satisfiability problems related to their complexity (Simon &amp; Dubois 1989; Crawford &amp; Auton 1993) and phase transitions in the expressiveness of Turing machines related to their complexity (Crutchfield &amp; Young 1989, 1990; Langton 1990; Dufort &amp; Lumsden 1994). 