Related papers: A Hypercomputation in Brouwer's Constructivism

Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible…

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this…

This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…

By the sometimes so-called MAIN THEOREM of Recursive Analysis, every computable real function is necessarily continuous. Weihrauch and Zheng (TCS'2000), Brattka (MLQ'2005), and Ziegler (ToCS'2006) have considered different relaxed notions…

We construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolutions, would contradict the Church-Turing thesis which lies at the foundation of computer…

In the paper a new programming construct, called concept, is introduced. Concept is pair of two classes: a reference class and an object class. Instances of the reference classes are passed-by-value and are intended to represent objects.…

A uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets, and uniformly continuous maps is presented. In work of Berger it was shown how to extract certified algorithms working with the signed…

Evolution by natural selection, which is one of the most compelling themes of modern science, brought forth evolutionary algorithms and evolutionary computation, applying mechanisms of evolution in nature to various problems solved by…

The concept of ``countable set'' is attributed to Georg Cantor, who set the boundary between countable and uncountable sets in 1874. The concept of ``computable set'' arose in the study of computing models in the 1930s by the founders of…

Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…

Counting the number of answers to conjunctive queries is a fundamental problem in databases that, under standard assumptions, does not have an efficient solution. The issue is inherently #P-hard, extending even to classes of acyclic…

The Universal Turing Machine (TM) is a model for VonNeumann computers --- general-purpose computers. A human brain can inside-skull-automatically learn a universal TM so that he acts as a general-purpose computer and writes a computer…

Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…

We prove a number of results motivated by global questions of uniformity in computability theory, and universality of countable Borel equivalence relations. Our main technical tool is a game for constructing functions on free products of…

We investigate partial functions and computability theory from within a constructive, univalent type theory. The focus is on placing computability into a larger mathematical context, rather than on a complete development of computability…

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in…

We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…

The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic…

In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…

We develop a general theory of jump operators, which is intended to provide an abstraction of the notion of "limit-computability" on represented spaces. Jump operators also provide a framework with a strong categorical flavor for…