相关论文: Internal Turing Machines

This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…

This paper explores and clarifies several issues surrounding Zeno machines and the issue of running a Turing machine for infinite time. Without a minimum hypothetical bound on physical conditions, any magical machine can be created, and…

We state a version of the P=?NP problem for infinite time Turing machines. It is observed that P not= NP for this version.

The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…

If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…

People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…

It is well known that the kind of P systems involved in the definition of the P conjecture is able to solve problems in the complexity class $\mathbf{P}$ by leveraging the uniformity condition. Here we show that these systems are indeed…

Turing Machines are universal computing machines in theory. It has been a long debate whether Turing Machines can simulate the consciousness mind behaviors in the materialistic universe. Three different hypotheses come out of such debate,…

Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard…

Infinite time Turing machines (ITTMs) have been introduced by Hamkins and Lewis in their seminal article arXiv:math/9808093. The strength of the model comes from a limit rule which allows the ITTM to compute through ordinal stages. This…

We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…

The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have…

We advance a Bayesian concept of 'intrinsic asymptotic universality' taking to its final conclusions previous conceptual and numerical work based upon a concept of a reprogrammability test and an investigation of the complex qualitative…

Although polynomial-time probabilistic Turing machines can utilize uncomputable transition probabilities to recognize uncountably many languages with bounded error when allowed to use logarithmic space, it is known that such "magic coins"…

This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…

The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical…

It is well-known that one-tape Turing machines working in linear time are no more powerful than finite automata, namely they recognize exactly the class of regular languages. We prove that it is not decidable if a one-tape machine works in…

The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical"…

Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which…

Can a problem undecidable with classical resources be decidable with quantum ones? The answer expected is no; as both being Turing theories, they should not solve the Halting problem - a problem unsolvable by any Turing machine. Yet, we…