Computability of Banach spaces is discussed. A compatible relation is shown to hold between the complex interpolation spaces of Calder) on (Studia Math. 24 (1964) 113) and the computability structures introduced by Pour-El and Richards (Computability in Analysis and Physics, Springer, Berlin, 1989). Namely, it is veri5ed that Calder) on’s original construction of the complex interpolation funct...

Computability logic is a formal theory of computability. The earlier article “Introduction to cirquent calculus and abstract resource semantics” by Japaridze proved soundness and completeness for the basic fragment CL5 of computability logic. The present article extends that result to the more expressive cirquent calculus system CL6, which is a conservative extension of both CL5 and classical p...

In Turing (1937) a characterization is given of those functions that can be computed using a mechanical device. Moreover it was shown that some precisely stated problems cannot be decided by such functions. In order to give evidence for the power of this model of computation, Turing showed in the same paper that machine computability has the same strength as definability via λ-calculus, introdu...

We revise and extend the foundation of computable topology in the framework of Type-2 theory of effectivity, TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations. We start from a computable topological space, which is a T0-space with a notation of a base such that in...

Quisani: Hello. It's that time of the year again when we have a discussion, isn't it? Author: Come on in. It is a busy time but I am happy to see you. Q: I am afraid my mood is rather critical today. A: That is all right. Speak your mind. Q: It is about computability and decidability. It seems to me that logicians' computability has little to do with real computability. Some so-called computabl...

We consider the informal concept of “computability” or “effective calculability” and twoof the formalisms commonly used to define it, “(Turing) computability” and“(general) recursiveness”. We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecia...

We propose a hierarchy of classes of functions that corresponds to the hierarchy of randomness notions. Each class of functions converges at the corresponding random points. We give various characterizations of the classes, that is, characterizations via integral tests, L-computability and layerwise computability. Furthermore, the relation among these classes is formulated using a version of So...

We present a survey of our work over the last few decades on generalizations of computability theory to many-sorted algebras. The following topics are discussed, among others: (1) abstract v concrete models of computation for such algebras; (2) computability and continuity, and the use of many-sorted topological partial algebras, containing the reals; (3) comparisons between various equivalent ...

Regular functions from infinite words to can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well deterministic two-way with look-ahead. In their one-way restriction, the latter define class of rational functions. Even though regular are robustly characterised several finite-state devices, even subclass may contain which not computable (by a Turing machine...

Abstract We investigate the computability (in sense of computable analysis) topological pressure P top ( ϕ ) on compact shift spaces X for continuous potentials ϕ : X → <mml:mi mathvariant="double-struc...