A semantic virtual machine (SVM) is a variant of a programable register machine that combines the transparency and simplicity of the action of a Turing machine with a clearly arranged assembler-style programming language and a user-friendly representation of semantic information. This paper describes the concept of the SVM, its memory management and flow control, and shows how a semantic virtua...

We present small polynomial time universal Turing machines with state-symbol pairs of (5, 5), (6, 4), (9, 3) and (18, 2). These machines simulate our new variant of tag system, the bi-tag system and are the smallest known universal Turing machines with 5, 4, 3 and 2-symbols respectively. Our 5-symbol machine uses the same number of instructions (22) as the smallest known universal Turing machin...

The author’s simple universal Turing machine requires the description of a specific Turing machine as data. In this article the coding of a specific Turing machine for unary multiplication is described. The description is a list of transitions with unary coded links between them. The order of the transitions in the list therefore makes a large difference in the size of the resulting code and th...

Certain Game of Life configurations create patterns. The most famous is the glider, a pattern of on and off cells that moves diagonally across the grid. It is possible to implement an arbitrary Turing machine by arranging Game of Life patterns. Computability theory applies to such Turing machines. Thus while not eluding the Game of Life rules, new laws (computability theory) that are independen...

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...