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Switch to: References
Citations of:
Hypercomputation: Computing more than the Turing machine
Dissertation, University of Melbourne (2002)
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The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation which claim to be able to solve the halting problem for Turing machines. We show that such arguments are flawed—a contradiction only occurs if a type of machine can compute its own diagonal function. We then demonstrate why such a situation (...) |
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For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to demonstrate this, these arguments lack the generality to be a satisfactory justification against the construction of any information-processing machine that computes beyond the universal Turing machine. To this end, I present a more (...) |
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The article analyses the role of Church’s Thesis (hereinafter CT) in the context of the development of hypercomputation research. The text begins by presenting various views on the essence of computer science and the limitations of its methods. Then CT and its importance in determining the limits of methods used by computer science is presented. Basing on the above explanations, the work goes on to characterize various proposals of hypercomputation showing their relative power in relation to the arithmetic hierarchy. The (...) No categories |
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Explainability and comprehensibility of AI are important requirements for intelligent systems deployed in real-world domains. Users want and frequently need to understand how decisions impacting them are made. Similarly it is important to understand how an intelligent system functions for safety and security reasons. In this paper, we describe two complementary impossibility results (Unexplainability and Incomprehensibility), essentially showing that advanced AIs would not be able to accurately explain some of their decisions and for the decisions they could explain people would (...) |
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This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess. 2005 Elsevier Inc. All rights reserved. |
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We show how to determine the k-th bit of Chaitin’s algorithmically random real number Ω by solving k instances of the halting problem. From this we then reduce the problem of determining the k-th bit of Ω to determining whether a certain Diophantine equation with two parameters, k and N , has solutions for an odd or an even number of values of N . We also demonstrate two further examples of Ω in number theory: an exponential Diophantine equation with (...) |
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