Related papers: Problem Theory
A suite of impressive scientific discoveries have been driven by recent advances in artificial intelligence. These almost all result from training flexible algorithms to solve difficult optimization problems specified in advance by teams of…
We critically review three major theories of machine learning and provide a new theory according to which machines learn a function when the machines successfully compute it. We show that this theory challenges common assumptions in the…
This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…
We investigate the mutation-selection dynamics for an evolutionary computation model based on Turing Machines that we introduced in a previous article. The use of Turing Machines allows for very simple mechanisms of code growth and code…
Based on Darwin's natural selection, we developed "machine scientists" to discover the laws of nature by learning from raw data. "Machine scientists" construct physical theories by applying a logic tree (state Decision Tree) and a value…
All natural things process and transform information. They receive environmental information as input, and transform it into appropriate output responses. Much of science is dedicated to building models of such systems -- algorithmic…
We position Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain kind must solve the halting problem for all programs of that…
A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system.…
We revisit the question (most famously) initiated by Turing: can human intelligence be completely modeled by a Turing machine? We show that the answer is \emph{no}, assuming a certain weak soundness hypothesis. More specifically we show…
What is the nature of curiosity? Is there any scientific way to understand the origin of this mysterious force that drives the behavior of even the stupidest naturally intelligent systems and is completely absent in their smartest…
Analyzed models of learning, which take into account that: 1) the rate of increase of student's knowledge is proportional to the difference between levels of teacher's requirements and prior knowledge; 2) if the requirements are too high,…
The notion of programming paradigms, with associated programming languages and methodologies, is a well established tenet of Computer Science pedagogy, enshrined in international curricula. However, this notion sits ill with Kuhn's classic…
The overarching theme of the following pages is that mathematical logic -- centered around the incompleteness theorems -- is first and foremost an investigation of $\textit{computation}$, not arithmetic. Guided by this intuition we will…
In this paper we present a novel tool to evaluate problem solving systems. Instead of using a system to solve a problem, we suggest using the problem to evaluate the system. By finding a numerical representation of a problem's complexity,…
The study of computability has its origin in Hilbert's conference of 1900, where an adjacent question, to the ones he asked, is to give a precise description of the notion of algorithm. In the search for a good definition arose three…
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…
This essay aims to propose construction theory, a new domain of theoretical research on machine construction, and use it to shed light on a fundamental relationship between living and computational systems. Specifically, we argue that…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
We apply the theory of learning to physically renormalizable systems in an attempt to develop a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…