相关论文: Infinite time computable model theory

One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…

Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…

We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…

In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an…

We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…

Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation studies models of computation…

We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing…

In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows…

This survey paper examines the effective model theory obtained with the BSS model of real number computation. It treats the following topics: computable ordinals, satisfaction of computable infinitary formulas, forcing as a construction…

Infinite Time Register Machines ($ITRM$'s) are a well-established machine model for infinitary computations. Their computational strength relative to oracles is understood, see e.g. Koepke (2009), Koepke and Welch (2011) and Koepke and…

Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of `standard' Quantum Computers. These approaches rely on and indicate that Quantum…

The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…

Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schr\"odinger…

The article contains an outline of a possible new direction for Computability Logic (see www.csc.villanova.edu/~japaridz/CL/ ), focused on computability without infinite memory or other impossible-to-possess computational resources. The new…

Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…

The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the…

This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…

The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only…

We survey aspects of prediction theory in infinitely many dimensions, with a view to the theory and applications of functional time series.

What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…