In this paper, we investigate the problem of synthesizing computable functions infinite words over an alphabet (data $\omega$-words). The notion computability is defined through Turing machines with inputs which can produce corresponding outputs in limit. We use non-deterministic transducers equipped registers, extension register automata outputs, to describe specifications. Being non-determini...

Although the formalizations of computability provided in the 1930s have proven to be equivalent, two different accounts of computability may be distinguished regarding computability as an epistemic concept. While computability, according to the epistemic account, should be based on epistemic constraints related to the capacities of human computers, the non-epistemic account considers computabil...

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded-lear...