We consider computations of a Turing machine under noise that causes violations of the transition function. Given an upper bound β on the size of bursts of faults, we construct a Turing machine M(β ) subject to faults that can simulate any fault-free machine under the condition that the time between bursts is lowerbounded by O(β 2).

We start with some definitions about probabilistic Turing machines (for a detailed exposition of this subject the reader is referred to [2]). Our basic model of computation is the Turing machine with input alphabet S z (0, l}. All machines are assumed to have two terminal states, namely q0 (reject) and 9, (accept). A probabilistic Turing machine (PTM) is syntactically the same as a nondetermini...

We show that, for all reasonable functions T (n) = o(n log n), we can algorithmically verify whether a given one-tape Turing machine runs in time at most T (n). This is a tight bound on the order of growth for the function T because we prove that, for T (n) ≥ (n+1) and T (n) = Ω(n log n), there exists no algorithm that would verify whether a given one-tape Turing machine runs in time at most T ...

Effective domain theory is applied to fuzzy logic to give suitable notions of semi-decidable and decidable L-subset. The connection with the notions of fuzzy Turing machines and fuzzy grammar given in literature is also investigated. This shows the inadequateness of these definitions and the difficulties in formulating an analogue of Church Thesis for fuzzy logic.

geometrical computation: Turing-computing ability and unpredictable accumulations (extended abstract) Jérôme Durand-Lose Mars 2004 Research Report N 2004-09 École Normale Supérieure de Lyon 46 Allée d’Italie, 69364 Lyon Cedex 07, France Téléphone : +33(0)4.72.72.80.37 Télécopieur : +33(0)4.72.72.80.80 Adresse électronique : [email protected] Abstract geometrical computation: Turing-computing abil...

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...