Related papers: Incomputability after Alan Turing
The relation between entropy and information has great significance for computation. Based on the strict reversibility of the laws of microphysics, Landauer (1961), Bennett (1973), Priese (1976), Fredkin and Toffoli (1982), Feynman (1985)…
Artificial computing machinery transforms representations through an objective process, to be interpreted subjectively by humans, so the machine and the interpreter are different entities, but in the putative natural computing both…
From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…
Computation has changed the world more than any previous expressions of knowledge. In its particular algorithmic embodiment, it offers a perspective, within which the digital computer (one of many possible) exercises a role reminiscent of…
Using the recently introduced universal computing model, called orchestrated machine, that represents computations in a dissipative environment, we consider a new kind of interpretation of Turing's Imitation Game. In addition we raise the…
According to the Church-Turing Thesis (CTT), effective formal behaviours can be simulated by Turing machines; this has naturally led to speculation that physical systems can also be simulated computationally. But is this wider claim true,…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…
In 1950, Alan Turing proposed an imitation game as the ultimate test of whether a machine was intelligent: could a machine imitate a human so well that its answers to questions indistinguishable from a human. Ever since, creating…
We investigate the Church-Kalm\'ar-Kreisel-Turing Theses concerning theoretical (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there…
Expanding upon the widely recognized notion of mathematical universality in Turing machines, a concept of thermodynamic universality in Turing machines is introduced. Under the physical Church-Turing thesis, the existence of a…
In 1950, Alan Turing proposed replacing the question "Can machines think?" with a behavioral test: if a machine's outputs are indistinguishable from those of a thinking being, the question of whether it truly thinks can be set aside. This…
John von Neumann's transformation from a logician of quantum mechanics (QM) in the 1920s to a natural philosopher of computation in the 1950s is discussed. The paper argues for revision of the historical image of Neumann to portray his…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
This paper reviews connections between physics and computation, and explores their implications. The main topics are computational "hardness" of physical systems, computational status of fundamental theories, quantum computation, and the…
The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…
In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the…
It is possible in principle to construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolution, would contradict the Church-Turing thesis, which lies at the…
Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of…