Related papers: A Tale of Two Turing Machines
The origin of the uncertainty inherent in quantum measurements has been discussed since quantum theory's inception, but to date the source of the indeterminacy of measurements performed at an angle with respect to a quantum state's…
Two objects are independent if they do not affect each other. Independence is well-understood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper…
A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system.…
Recently the field of Human-Robot Interaction gained popularity, due to the wide range of possibilities of how robots can support humans during daily tasks. One form of supportive robots are socially assistive robots which are specifically…
The power of real-time Turing machines using sublinear space is investigated. In contrast to a claim appearing in the literature, such machines can accept non-regular languages, even if working in deterministic mode. While maintaining a…
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantum computers is under active…
The question of whether artificial beings or machines could become self-aware or consciousness has been a philosophical question for centuries. The main problem is that self-awareness cannot be observed from an outside perspective and the…
This paper is an experimental exploration of the relationship between the runtimes of Turing machines and the length of proofs in formal axiomatic systems. We compare the number of halting Turing machines of a given size to the number of…
Artificial computing machinery transforms representations through an objective process, to be interpreted subjectively by humans, so the machine and the interpreter are different entities, but in the putative natural computing both…
We answer two questions posed by Castro and Cucker, giving the exact complexities of two decision problems about cardinalities of omega-languages of Turing machines. Firstly, it is $D_2(\Sigma_1^1)$-complete to determine whether the…
There are enormous amount of examples of Computation in nature, exemplified across multiple species in biology. One crucial aim for these computations across all life forms their ability to learn and thereby increase the chance of their…
Machine translation (MT) plays an important role in benefiting linguists, sociologists, computer scientists, etc. by processing natural language to translate it into some other natural language. And this demand has grown exponentially over…
The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
We revisit the question (most famously) initiated by Turing: can human intelligence be completely modeled by a Turing machine? We show that the answer is \emph{no}, assuming a certain weak soundness hypothesis. More specifically we show…
To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared…
An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…
A tower between two regular languages is a sequence of strings such that all strings on odd positions belong to one of the languages, all strings on even positions belong to the other language, and each string can be embedded into the next…
We position Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain kind must solve the halting problem for all programs of that…
Recent developments in explainable artificial intelligence promise the potential to transform human-robot interaction: Explanations of robot decisions could affect user perceptions, justify their reliability, and increase trust. However,…