We answer two questions posed by Castro and Cucker in [CC89], giving the exact complexities of two decision problems about cardinalities of ω-languages of Turing machines. Firstly, it is D2(Σ 1 1 )-complete to determine whether the ω-language of a given Turing machine is countably infinite, where D2(Σ 1 1 ) is the class of 2-differences of Σ 1 -sets. Secondly, it is Σ 1 -complete to determine w...

Recently, among experiments for realization of quantum computers, NMR quantum computers have achieved the most impressive succession. There is a model of the NMR quantum computation by Atsumi and Nishino’s bulk quantum Turing machine. It assumes, however, an unnatural assumption with quantum mechanics. We, then, define a more natural and quantum mechanically realizable modified bulk quantum Tur...

Alan Turing proposed an interactive test to replace the question \Can machines think?" This test has become known as the Turing Test and its validity for determining intelligence or thinking is still in question. Struggling with the validity of long proofs, program correctness, computational complexity and cryptography, theoreticians developed interactive proof systems. By formalizing the Turin...

This issue of the Kybernetes journal is concerned with the philosophical question Can a Machine Think? Famously, in his 1950 paper ‘Computing Machinery and Intelligence’ [11], the British mathematician Alan Turing suggested replacing this question which he found “too meaningless to deserve discussion” with a simple [behaviourial] test based on an imagined Victorian-esque pastime he entitled the...

Turing showed the existence of a model universal for the set of Turing machines in the sense that given an encoding of any Turing machine as input the universal Turing machine simulates it. We introduce the concept of universality for reactive systems and construct a ccs process universal in the sense that, given an encoding of any ccs process, it behaves like this process up to weak bisimulati...

Our model of computation (theoretical machine) was designed for the analysis of analog Fourier optical processors, its basic data unit being a continuous image of unbounded resolution. In this paper, we demonstrate the universality of our machine by presenting a framework for arbitrary Turing machine simulation. Computational complexity bene ts are also demonstrated by providing a O(log2n) algo...

Computability concerns information with a causal – typically algorithmic – structure. As such, it provides a schematic analysis of many naturally occurring situations. We look at ways in which computabilitytheoretic structure emerges in natural contexts. We will look at how algorithmic structure does not just emerge mathematically from information, but how that emergent structure can model the ...

Turing showed the existence of a model universal for the set of Turing machines in the sense that given an encoding of any Turing machine as input the universal Turing machine simulates it. We introduce the concept of univer-sality for reactive systems and construct a ccs process universal in the sense that, given an encoding of any ccs process, it behaves like this process up to weak bisimulat...