Related papers: A Distributed Extension of the Turing Machine
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…
Many applications from camera arrays to sensor networks require efficient compression and processing of correlated data, which in general is collected in a distributed fashion. While information-theoretic foundations of distributed…
Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation studies models of computation…
The framework of distributed computing, consisting of several spatially separated input-output servers, has immense importance in distant data manipulation. One of the most challenging parts of this setting is to optimize the use of…
This article presents an artificial intelligence (AI) architecture intended to simulate the iterative updating of the human working memory system. It features several interconnected neural networks designed to emulate the specialized…
This paper shows that the programming model of Babbage's Analytical Engine, although unconventional, can be harnessed in order to simulate indirect addressing, a capability that was not included in the original instruction set. That is, in…
In the era of intelligent computing, computational progress in text processing is an essential consideration. Many systems have been developed to process text over different languages. Though, there is considerable development, they still…
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
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…
MemComputing is a new model of computation that exploits the non-equilibrium property-we call 'memory'-of any physical system to respond to external perturbations by keeping track of how it has reacted at previous times. Its digital,…
The input/output complexity, which is the complexity of data exchange between the main memory and the external memory, has been elaborately studied by a lot of former researchers. However, the existing works failed to consider the…
Real-life agents seldom have unlimited reasoning power. In this paper, we propose and study a new formal notion of computationally bounded strategic ability in multi-agent systems. The notion characterizes the ability of a set of agents to…
One of the roots of evolutionary computation was the idea of Turing about unorganized machines. The goal of this work is the development of foundations for evolutionary computations, connecting Turing's ideas and the contemporary state of…
In the manuscript titled "Computation environment (1)", we introduced a notion called computation environment as an interactive model for computation and complexity theory. In this model, Turing machines are not autonomous entities and find…
While the digital twin has become an intrinsic part of the product creation process, its true power lies in the connectivity of the digital representation with its physical counterpart. Data acquired on the physical asset can validate,…
The ongoing exponential rise in recording capacity calls for new approaches for analysing and interpreting neural data. Effective dimensionality has emerged as an important property of neural activity across populations of neurons, yet…
Natural language is inherently a discrete symbolic representation of human knowledge. Recent advances in machine learning (ML) and in natural language processing (NLP) seem to contradict the above intuition: discrete symbols are fading…
We report a new limitation on the ability of physical systems to perform computation -- one that is based on generalizing the notion of memory, or storage space, available to the system to perform the computation. Roughly, we define memory…
Deep neural networks have shown the ability to extract universal feature representations from data such as images and text that have been useful for a variety of learning tasks. However, the fruits of representation learning have yet to be…