text: We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice. Cons-freeness roughly means that data constructors cannot occur in function bodies and all manipulation of storage space thus has to happen indirectly using the call stack. While cons-free programs have previously been used by several au thors to characterise complexity classes, the work on non-deterministic programs has almost exclusively considered programs of data order 0. Previous work has shown that adding explicit non-determinism to cons-free programs taking data of order 0 does not increase expressivity; we prove that this - dramatically - is not the case for higher data orders: adding non-determinism to programs with data order at least 1 allows for a characterisation of the entire class of elementary-time decidable sets.
  @cite_13: We give a recursion-theoretic characterization of FP which describes polynomial time computation independently of any externally imposed resource bounds. In particular, this syntactic characterization avoids the explicit size bounds on recursion (and the initial function 2|x|·|y|) of Cobham.
  @cite_4: 
  @cite_12: Abstract An implicit characterization of the class NP is given, without using any minimization scheme. This is the first purely recursion-theoretic formulation of NP .
summary: Characterisation of non-deterministic complexity classes via programming languages remains a largely unexplored area. Bellantoni obtained a characterisation of @math in his dissertation @cite_4 using similar approaches as @cite_13 , but at the cost of having a minimisation operator (as in recursion theory), a restriction later removed by Oitavem @cite_12 . A general framework for implicitly characterising a larger hierarchy of non-deterministic classes remains an open problem.