An introduction to feedback Turing computability

2020 ◽  
Vol 30 (1) ◽  
pp. 27-60
Author(s):  
Nathanael L Ackerman ◽  
Cameron E Freer ◽  
Robert S Lubarsky
Keyword(s):  
Turing Computability

Abstract Feedback computability is computation with an oracle that contains the correct convergence/divergence information for all computations calling that same oracle. Here we study feedback Turing computability, as well as feedback for some smaller classes of computation. We also examine some versions of parallelization of these notions.

The Equivalence of Turing-Computability and µ-Recursiveness

1969 ◽  
pp. 93-112
Author(s):  
Hans Hermes
Keyword(s):  
Turing Computability

Turing Computability

2012 ◽  
pp. 23-34
Author(s):  
George S. Boolos ◽  
John P. Burgess ◽  
Richard C. Jeffrey
Keyword(s):  
Turing Computability

scholarly journals Feedback Turing Computability, and Turing Computability as Feedback

2015 ◽  
Author(s):  
Nathanael L. Ackerman ◽  
Cameron E. Freer ◽  
Robert S. Lubarsky
Keyword(s):  
Turing Computability

scholarly journals REPRESENTATIONS AND CHARACTERIZATIONS OF LANGUAGES IN CHOMSKY HIERARCHY BY MEANS OF INSERTION-DELETION SYSTEMS

2008 ◽  
Vol 19 (04) ◽  
pp. 859-871 ◽  
Author(s):  
GHEORGHE PĂUN ◽  
MARIO J. PÉREZ-JIMÉNEZ ◽  
TAKASHI YOKOMORI
Keyword(s):  
Dna Computing ◽  
Research Direction ◽  
Regular Languages ◽  
Turing Computability ◽  
Chomsky Hierarchy ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Language L ◽  
Context Free

Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability and characterizations or representations of languages in Chomsky hierarchy were obtained in this framework. In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Schützenberger representation of context-free languages, i.e., in the form L = h(L(γ) ∩ D), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages – this time using insertion systems of weight (3, 0) and star languages.

scholarly journals TRANSCENDING THE LIMITS OF TURING COMPUTABILITY

2004 ◽  
Author(s):  
VADIM A. ADAMYAN ◽  
CRISTIAN S. CALUDE ◽  
BORIS S. PAVLOV
Keyword(s):  
Turing Computability

Turing Computability

2016 ◽  
Author(s):  
Robert I. Soare
Keyword(s):  
Turing Computability

The Equivalence of Turing-Computability and μ-Recursiveness

1965 ◽  
pp. 93-112
Author(s):  
Hans Hermes
Keyword(s):  
Turing Computability

Computation, Dynamics, and Cognition

1997 ◽  
Author(s):  
Marco Giunti
Keyword(s):  
Dynamical Systems ◽  
Cognitive Science ◽  
Scientific Explanation ◽  
Cognitive Systems ◽  
Computational System ◽  
Turing Computability ◽  
Conceptual Foundation ◽  
Philosophical Perspective ◽  
Dynamical Approach ◽  
Computation Theory

Currently there is growing interest in the application of dynamical methods to the study of cognition. Computation, Dynamics, and Cognition investigates this convergence from a theoretical and philosophical perspective, generating a provocative new view of the aims and methods of cognitive science. Advancing the dynamical approach as the methodological frame best equipped to guide inquiry in the field's two main research programs--the symbolic and connectionist approaches--Marco Giunti engages a host of questions crucial not only to the science of cognition, but also to computation theory, dynamical systems theory, philosophy of mind, and philosophy of science. In chapter one Giunti employs a dynamical viewpoint to explore foundational issues in computation theory. Using the concept of Turing computability, he precisely and originally defines the nature of a computational system, sharpening our understanding of computation theory and its applications. In chapter two he generalizes his definition of a computational system, arguing that the concept of Turing computability itself is relative to the kind of support on which Turing machine operate. Chapter three completes the book's conceptual foundation, discussing a form of scientific explanation for real dynamical systems that Giunti calls "Galilean explanation." The book's fourth and final chapter develops the methodological thesis that all cognitive systems are dynamical systems. On Giunti's view, a dynamical approach is likely to benefit even those scientific explanations of cognition which are based on symbolic models. Giunti concludes by proposing a new modeling practice for cognitive science, one based on "Galilean models" of cognitive systems. Innovative, lucidly-written, and broad-ranging in its analysis, Computation, Dynamics, and Cognition will interest philosophers of science and mind, as well as cognitive scientists, computer scientists, and theorists of dynamical systems. This book elaborates a comprehensive picture of the application of dynamical methods to the study of cognition. Giunti argues that both computational systems and connectionist networks are special types of dynamical systems. He shows how this dynamical approach can be applied to problems of cognition, information processing, consciousness, meaning, and the relation between body and mind.

scholarly journals AN ANATOMY OF A QUANTUM ADIABATIC ALGORITHM THAT TRANSCENDS THE TURING COMPUTABILITY

2005 ◽  
Vol 03 (01) ◽  
pp. 177-182 ◽  
Author(s):  
TIEN D. KIEU
Keyword(s):  
Turing Computability ◽  
Hilbert's Tenth Problem ◽  
Hilbert’S Tenth Problem

We give an update on a quantum adiabatic algorithm for the Turing noncomputable Hilbert's tenth problem, and briefly go over some relevant issues and misleading objections to the algorithm.

Sign in / Sign up

Export Citation Format

Share Document