Decision Problems For Turing Machines

We answer two questions posed by Castro and Cucker, giving the exact complexities of two decision problems about cardinalities of omega-languages of Turing machines. Firstly, it is $D_2(\Sigma_1^1)$-complete to determine whether the omega-language of a given Turing machine is countably infinite, where $D_2(\Sigma_1^1)$ is the class of 2-differences of $\Sigma_1^1$-sets. Secondly, it is $\Sigma_1^1$-complete to determine whether the omega-language of a given Turing machine is uncountable.Comment: To appear in Information Processing Letter

On The Foundations of Digital Games

Computers have lead to a revolution in the games we play, and, following this, an interest for computer-based games has been sparked in research communities. However, this easily leads to the perception of a one-way direction of influence between that the field of game research and computer science. This historical investigation points towards a deep and intertwined relationship between research on games and the development of computers, giving a richer picture of both fields. While doing so, an overview of early game research is presented and an argument made that the distinction between digital games and non-digital games may be counter-productive to game research as a whole

The Turing Test and the Zombie Argument

In this paper I shall try to put some implications concerning the Turing's test and the so-called Zombie arguments into the context of philosophy of mind. My intention is not to compose a review of relevant concepts, but to discuss central problems, which originate from the Turing's test - as a paradigm of computational theory of mind - with the arguments, which refute sustainability of this thesis. In the first section (Section I), I expose the basic computationalist presuppositions; by examining the premises of the Turing Test (TT) I argue that the TT, as a functionalist paradigm concept, underlies the computational theory of mind. I treat computationalism as a thesis that defines the human cognitive system as a physical, symbolic and semantic system, in such a manner that the description of its physical states is isomorphic with the description of its symbolic conditions, so that this isomorphism is semantically interpretable. In the second section (Section II), I discuss the Zombie arguments, and the epistemological-modal problems connected with them, which refute sustainability of computationalism. The proponents of the Zombie arguments build their attack on the computationalism on the basis of thought experiments with creatures behaviorally, functionally and physically indistinguishable from human beings, though these creatures do not have phenomenal experiences. According to the consequences of these thought experiments - if zombies are possible, then, the computationalism doesn't offer a satisfying explanation of consciousness. I compare my thesis from Section 1, with recent versions of Zombie arguments, which claim that computationalism fails to explain qualitative phenomenal experience. I conclude that despite the weaknesses of computationalism, which are made obvious by zombie-arguments, these arguments are not the last word when it comes to explanatory force of computationalism

Playing Smart - Artificial Intelligence in Computer Games

Abstract: With this document we will present an overview of artificial intelligence in general and artificial intelligence in the context of its use in modern computer games in particular. To this end we will firstly provide an introduction to the terminology of artificial intelligence, followed by a brief history of this field of computer science and finally we will discuss the impact which this science has had on the development of computer games. This will be further illustrated by a number of case studies, looking at how artificially intelligent behaviour has been achieved in selected games

The "paradox" of computability and a recursive relative version of the Busy Beaver function

In this article, we will show that uncomputability is a relative property not only of oracle Turing machines, but also of subrecursive classes. We will define the concept of a Turing submachine, and a recursive relative version for the Busy Beaver function which we will call Busy Beaver Plus function. Therefore, we will prove that the computable Busy Beaver Plus function defined on any Turing submachine is not computable by any program running on this submachine. We will thereby demonstrate the existence of a "paradox" of computability a la Skolem: a function is computable when "seen from the outside" the subsystem, but uncomputable when "seen from within" the same subsystem. Finally, we will raise the possibility of defining universal submachines, and a hierarchy of negative Turing degrees.Comment: 10 pages. 0 figures. Supported by the National Council for Scientific and Technological Development (CNPq), Brazil. Book chapter published in Information and Complexity, Mark Burgin and Cristian S. Calude (Editors), World Scientific Publishing, 2016, ISBN 978-981-3109-02-5, available at http://www.worldscientific.com/worldscibooks/10.1142/10017. arXiv admin note: substantial text overlap with arXiv:1612.0522