Ultraparallelism Constructive Methods. From P to CC

The purpose of this paper is to understand what delimits computation. The classical notion of computation formulated in the Church-Turing Thesis seems to suggest that computability is a mathematical concept. Physicists David Deutsch points out that there is a physical assertion to this claim. We will discuss this claim and its consequences. Moreover, we will discuss what happens when the boundaries of what it computable get stretched too far. In that respect, we will look at hypercompuation. Lastly, I will discuss a paper by Andrew Hodges in which he criticises hypercomputation. In the end, we will answer the question as to what extent the limits of computation are physical and how the mathematical aspects of computation as developed by Church and Turing relate to the concept's physical limitations.

Mathematics, 2022

This paper shows some of the differences and similarities between computation and hypercomputation, the similarities relating to the complexity of propositional computation and the differences being the propositions that can be decided computationally or hypercomputationally. The methods used are ordinal Turing machines with infinitely long programs and diagonalization out of computing complexity classes. The main results are the characterization of inequalities of run time complexities of serial, indeterministic serial and parallel computers and hypercomputers and the specification of a hierarchy of hypercomputers that can hypercompute the truths of all propositions in the standard class model of set theory, the von Neumann hierarchy of pure sets.

International Journal of Scientific Research in Computer Science, Engineering and Information Technology, 2020

The main purpose of this paper is to examine some (potential) applications of quantum computation in AI and to review the interplay between quantum theory and AI. For the readers who are not familiar with quantum computation, a brief introduction to it is provided, and a famous but simple quantum algorithm is introduced so that they can appreciate the power of quantum computation. Also, a (quite personal) survey of quantum computation is presented in order to give the readers a (unbalanced) panorama of the field. The author hopes that this paper will be a useful map for AI researchers who are going to explore further and deeper connections between AI and quantum computation as well as quantum theory although some parts of the map are very rough and other parts are empty, and waiting for the readers to fill in.

Minds and Machines, 2010

In their joint paper entitled ''The Replication of the Hard Problem of Consciousness in AI and BIO-AI'' (Boltuc et al. Replication of the hard problem of conscious in AI and Bio-AI: An early conceptual framework 2008), Nicholas and Piotr Boltuc suggest that machines could be equipped with phenomenal consciousness, which is subjective consciousness that satisfies Chalmer's hard problem (We will abbreviate the hard problem of consciousness as ''H-consciousness''). The claim is that if we knew the inner workings of phenomenal consciousness and could understand its' precise operation, we could instantiate such consciousness in a machine. This claim, called the extra-strong AI thesis, is an important claim because if true it would demystify the privileged access problem of first-person consciousness and cast it as an empirical problem of science and not a fundamental question of philosophy. A core assumption of the extra-strong AI thesis is that there is no logical argument that precludes the implementation of H-consciousness in an organic or in-organic machine provided we understand its algorithm. Another way of framing this conclusion is that there is nothing special about H-consciousness as compared to any other process. That is, in the same way that we do not preclude a machine from implementing photosynthesis, we also do not preclude a machine from implementing H-consciousness. While one may be more difficult in practice, it is a problem of science and engineering, and no longer a philosophical question. I propose that Boltuc's conclusion, while plausible and convincing, comes at a very high price; the argument given for his conclusion does not exclude any conceivable process from machine implementation. In short, if we make some assumptions about the equivalence of a rough notion of algorithm and then tie this to human understanding, all logical preconditions vanish and the argument grants that any process can be implemented in a machine. The purpose of this paper is to comment on the argument for his conclusion and offer additional properties of

Emergence, Complexity and Computation, 2016

We present a simple example that disproves the universality principle. Unlike previous counterexamples to computational universality, it does not rely on extraneous phenomena, such as the availability of input variables that are time varying, computational complexity that changes with time or order of execution, physical variables that interact with each other, uncertain deadlines, or mathematical conditions among the variables that must be obeyed throughout the computation. In the most basic case of the new example, all that is used is a single pre-existing global variable whose value is modified by the computation itself. In addition, our example offers a new dimension for separating the computable from the uncomputable, while illustrating the power of parallelism in computation. Keywords and phrases: nonuniversality in computation; universal computer; simulation; models of computation; time unit; time-varying variables; time-varying computational complexity; rank-varying computational complexity; interacting variables; uncertain time constraints; mathematical constraints; finite and fixed number of operations per time unit, general-purpose computer; finiteness condition; unbounded space; unbounded time; communication with the outside world; Turing Machine; Random Access Machine; Parallel Random Access Machine.

Theoretical Computer Science, 2004

… Proceedings of the Conference Held at …, 1986

1998

s of the Poster Session Contributions to the First International Conference on Unconventional Models of Computation Centre for Discrete Mathematics and Theoretical Computer Science, NZ and Santa Fe Institute, USA 5 # 9 January 1998, Auckland, New Zealand Edited by Peter Hertling, University of Auckland Preface The First International Conference on Unconventional Models of Computation, UMC'98, organized by the Centre for Discrete Mathematics and Theoretical Computer Science, in cooperation with the Santa Fe Institute, was held at the University of Auckland from January 5#9, 1998. The proceedings of UMC'98 have appeared in the DMTCS Series of Springer#Verlag, Singapore. This CDMTCS Research Report contains the abstracts or extended abstracts of the poster session contributions to UMC'98. They cover engineering, physical, mathematical, and philosophical aspects of a broad range of unconventional models of computation: from evolutionary computation, quantum computation, D...

2002