Related papers: Problem Theory
In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete…
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century there have been remarkable advances in the development of theory for this diversification, and the theory's success…
The main deficiency of the algorithms running on digital computers nowadays is their inability to change themselves during the execution. In line with this, the paper introduces the so-called replicated algorithms, inspired by the concept…
The ability to interpret the mental state of another agent based on its behavior, also called Theory of Mind (ToM), is crucial for humans in any kind of social interaction. Artificial systems, such as intelligent assistants, would also…
In this paper, we make a preliminary interpretation of Cook's theorem presented in [1]. This interpretation reveals cognitive biases in the proof of Cook's theorem that arise from the attempt of constructing a formula in CNF to represent a…
This study aims to extend the framework for assessing artificial intelligence, called GROW-AI (Growth and Realization of Autonomous Wisdom), designed to answer the question "Can machines grow up?" -- a natural successor to the Turing Test.…
This chapter aims to provide next-level understanding of the problems of the world and the solutions available to those problems, which lie very well within the domain of neural computing, and at the same time are intelligent in their…
Generative AI techniques have opened the path for new generations of machines in diverse domains. These machines have various capabilities for example, they can produce images, generate answers or stories, and write codes based on 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,…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
Computational modeling plays an increasingly important role in neuroscience, highlighting the philosophical question of how computational models explain. In the context of neural network models for neuroscience, concerns have been raised…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
This note introduces a generalization to the setting of infinite-time computation of the busy beaver problem from classical computability theory, and proves some results concerning the growth rate of an associated function. In our view,…
Any problem is concerned with the mind, but what do minds make a decision on? Here we show that there are three conditions for the mind to make a certain answer. We found that some difficulties in physics and mathematics are in fact…
Characterising the intelligence of biological organisms is challenging. This work considers intelligent algorithms developed evolutionarily within neural systems. Mathematical analyses unveil a natural equivalence between canonical neural…
Turing Machines are universal computing machines in theory. It has been a long debate whether Turing Machines can simulate the consciousness mind behaviors in the materialistic universe. Three different hypotheses come out of such debate,…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
In the present paper, we construct what we call a pedagogical universal Turing machine. We try to understand which comparisons with biological phenomena can be deduced from its encoding and from its working.
The human brain is the substrate for human intelligence. By simulating the human brain, artificial intelligence builds computational models that have learning capabilities and perform intelligent tasks approaching the human level. Deep…