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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…
Many problems in science and engineering are optimization problems, which may require sophisticated optimization techniques to solve. Nature-inspired algorithms are a class of metaheuristic algorithms for optimization, and some algorithms…
Automatic Programming is one of the most important areas of computer science research today. Hardware speed and capability have increased exponentially, but the software is years behind. The demand for software has also increased…
The halting probability of a Turing machine,also known as Chaitin's Omega, is an algorithmically random number with many interesting properties. Since Chaitin's seminal work, many popular expositions have appeared, mainly focusing on the…
Universal Turing Machines [29, 10, 18] are well known in computer science but they are about manual programming for general purposes. Although human children perform conscious learning (i.e., learning while being conscious) from infancy…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
The release of openly available, robust natural language generation algorithms (NLG) has spurred much public attention and debate. One reason lies in the algorithms' purported ability to generate human-like text across various domains.…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations.…
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,…
Existing theoretical universal algorithmic intelligence models are not practically realizable. More pragmatic approach to artificial general intelligence is based on cognitive architectures, which are, however, non-universal in sense that…
Infinite time Turing machines extend the classical Turing machine concept to transfinite ordinal time, thereby providing a natural model of infinitary computability that sheds light on the power and limitations of supertask algorithms.
Programming languages are engineered languages that allow to instruct a machine and share algorithmic information; they have a great influence on the society since they underlie almost every information technology artefact, and they are at…
Most work on computational complexity is concerned with time. However this course will try to show that program-size complexity, which measures algorithmic information, is of much greater philosophical significance. I'll discuss how one can…
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered…
A number of optimization algorithms have been inspired by the physics of Newtonian motion. Here, we ask the question: do algorithms themselves obey some ``natural laws of motion,'' and can they be derived by an application of these laws? We…
Language models now provide an interface to express and often solve general problems in natural language, yet their ultimate computational capabilities remain a major topic of scientific debate. Unlike a formal computer, a language model is…
At present, artificial intelligence in the form of machine learning is making impressive progress, especially the field of deep learning (DL) [1]. Deep learning algorithms have been inspired from the beginning by nature, specifically by the…