Abstract In this survey we discuss work of Levin and V’yugin on collections sequences that are non-negligible in the sense they can be computed by a probabilistic algorithm with positive probability. More precisely, introduced an ordering closed under Turing equivalence. Roughly speaking, given two such $\mathcal {A}$ {B}$ , is below if {A}\setminus \mathcal negligible. The degree structure ass...

We discuss the conceptual problem of identifying the natural notions of computability at higher types (over the natural numbers). We argue for an eclectic approach, in which one considers a wide range of possible approaches to defining higher type computability and then looks for regularities. As a first step in this programme, we give an extended survey of the different strands of research on ...

We generalize the standard construction of realizability models (specifically, of categories of assemblies) to a wide class of computability structures, broad enough to embrace models of computation such as labelled transition systems and process algebras. We consider a general notion of simulation between such computability structures, and show how these simulations correspond precisely to cer...