Related papers: Intrinsic Smallness
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
Our main models of computation (the Turing Machine and the RAM) make fundamental assumptions about which primitive operations are realizable. The consensus is that these include logical operations like conjunction, disjunction and negation,…
Our goal is to construct mathematical operations that combine indeterminism measured from quantum randomness with computational determinism so that non-mechanistic behavior is preserved in the computation. Formally, some results about…
A mathematical concept is identified and analyzed that is implicit in the 2012 paper Turing Incomputable Computation, presented at the Alan Turing Centenary Conference (Turing-100, Manchester). The concept, called dynamic level sets, is…
We study the logical content of several maximality principles related to the finite intersection principle ($F\IP$) in set theory. Classically, these are all equivalent to the axiom of choice, but in the context of reverse mathematics their…
Interest in the thermodynamics of computation has revived in recent years, driven by developments in science, economics and technology. Given the consequences of the growing demand for computational power, the idea of reducing the energy…
It is possible to enumerate all computer programs. In particular, for every partial computable function, there is a shortest program which computes that function. f-MIN is the set of indices for shortest programs. In 1972, Meyer showed that…
This short survey of recent work in tile self-assembly discusses the use of simulation to classify and separate the computational and expressive power of self-assembly models. The journey begins with the result that there is a single…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
In this article we call a sequence $(a_n)_n$ of elements of a metric space nearly computably Cauchy if for every strictly increasing computable function $r:\mathbb{N}\to\mathbb{N}$ the sequence $(d(a_{r(n+1)},a_{r(n)}))_n$ converges…
This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly…
To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a…
Superintelligence is a hypothetical agent that possesses intelligence far surpassing that of the brightest and most gifted human minds. In light of recent advances in machine intelligence, a number of scientists, philosophers and…
A coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse…
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…
Given partial information about a set, we are interested in fully recovering the original set from what is given. If a set encodes itself robustly, any partial information about the set suffices to fully recover the information about the…
Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
There is a cognitive limit in Human Mind. This cognitive limit has played a decisive role in almost all fields including computer sciences. The cognitive limit replicated in computer sciences is responsible for inherent Computational…