The Decidable Properties of Subrecursive Functions

Mathieu Hoyrup, Marc Herbstritt
2016 International Colloquium on Automata, Languages and Programming  
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 and
more » ... dable properties can be obtained as combinations of two classes of basic decidable properties: (i) the function takes some particular values on a finite set of inputs, and (ii) every finite part of the function can be compressed to some extent.
doi:10.4230/lipics.icalp.2016.108 dblp:conf/icalp/Hoyrup16 fatcat:k2xljz6l6zhptdslbue7nfsc7a