相关论文: Leibniz, Randomness and the Halting Probability
Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and…
The purpose of this thesis is to make an analysis of the concept of Hypercomputation and of some hypermachines. This thesis is separated in three main parts. We start in the first chapter with an analysis of the concept of Classical…
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a…
This essay explores the limits of Turing machines concerning the modeling of minds and suggests alternatives to go beyond those limits.
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…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
Unlike Martin-L\"of randomness and Schnorr randomness, computable randomness has not been defined, except for a few ad hoc cases, outside of Cantor space. This paper offers such a definition (actually, several equivalent definitions), and…
By closely rereading the original Turing's 1936 article, we can gain insight about that it is based on the claim to have defined a number which is not computable, arguing that there can be no machine computing the diagonal on the…
The blog focusses on algorithmic randomness and its connections to quantum information theory, group theory and its connections to logic, and computability analogs of cardinal characteristics.
Work in progress concerning alternative formalizations of arithmetic.
In the wake of the latest trends of artificial intelligence (AI), there has been a resurgence of claims and questions about the Turing test and its value, which are reminiscent of decades of practical "Turing" tests. If AI were quantum…
A brief remembrance of some aspects of the author's scientific interaction with Stephen Hawking. A contribution to Physics Today's March 14, 2018 web page in which Stephen Hawking is remembered by his colleagues.
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…
This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that…
The Turing machine (TM) and the Church thesis have formalized the concept of computable number, this allowed to display non-computable numbers. This paper defines the concept of number "approachable" by a TM and shows that some (if not all)…
Toby Walsh in 'The Singularity May Never Be Near' gives six arguments to support his point of view that technological singularity may happen but that it is unlikely. In this paper, we provide analysis of each one of his arguments and arrive…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
Was Einstein wrong? This paper provides a detailed technical review of Einstein's special and general relativity from an astrophysical perspective, including the historical development of the theories, experimental tests, modern…