Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multi-fuzzy set (i.e. an orthogonal approach to the fuzzification of multisets), we introduce two variants of P systems with fuzzy co...

We resolve an old problem, namely to design a ‘natural’ machine model for accepting the complements of recursively enumerable languages. The model we present is based on Turing machines with ‘onesided’ advice, which are Turing machines with advice with a restricted scenario for the use of their advice during computations. We show that Turing machines with one-sided advice accept precisely the c...

We prove that there is no algorithm to tell whether an arbitrarily constructed Quantum Turing Machine has same time steps for different branches of computation. We, hence, can not avoid the notion of halting to be probabilistic in Quantum Turing Machine. Our result suggests that halting scheme of Quantum Turing Machine and quantum complexity theory based upon the existing halting scheme sholud ...

The Church-Turing thesis 2 states that to be computable is to be computable by a Turing machine and the modern discipline in computational complexity theory states that to be efficiently computable is to be computable by a Turing machine within polynomial steps in the length of the input data. However, Feynman pointed out that a Turing machine cannot simulate a quantum mechanical process effici...

The -rst attempts concerning formalization of the notion of fuzzy algorithms in terms of Turing machines are dated in late 1960s when this notion was introduced by Zadeh. Recently, it has been observed that corresponding so-called classical fuzzy Turing machines can solve undecidable problems. In this paper we will give exact recursion-theoretical characterization of the computational power of ...

The theory of Kolmogorov complexity is based on the discovery, by Alan Turing in 1936, of the universal Turing machine. After proposing the Turing machine as an explanation of the notion of a computing machine, Turing found that there exists one Turing machine which can simulate any other Turing machine. Complexity, according to Kolmogorov, can be measured by the length of the shortest program ...

In this brief note, we give a simple information-theoretic proof that 2-state 3-color universal Turing machines don’t exist. Let us suppose that there exists a 2-state 3-color universal Turing machine U (without a halting state). Then it must be possible to program U to emulate any Turing machine T (without a halting state) by initializing the tape of U with a string of colors that specify both...

In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behaviour of cellular automata, that the computational basis for modeling this region is the Universal Turing Machine. In this paper, following a suggestion of Crutchfield, we try to show that the Turing machine model ...

Turing machines have been well studided in the context of Computability theory, looking at computations starting from a very specific state and a given input. We intend to study here Turing machines from the point of view of dynamical systems, that is consider Turing machines starting from any input, and any possible state. This model is very interesting from this point of view, and intimately ...