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What can be decided or semidecided about a primitive recursive function, given a definition of that function by primitive recursion? What about subrecursive classes other than primitive recursive functions? We provide a complete and explicit characterization of the decidable and semidecidable properties. This characterization uses a variant of Kolmogorov complexity where only programs in a subrecursive programming language are allowed. More precisely, we prove that all the decidable anddoi:10.4230/lipics.icalp.2016.108 dblp:conf/icalp/Hoyrup16 fatcat:k2xljz6l6zhptdslbue7nfsc7a