Related papers: An algorithm to simulate alternating Turing machin…
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…
The architecture of neural Turing machines is differentiable end to end and is trainable with gradient descent methods. Due to their large unfolded depth Neural Turing Machines are hard to train and because of their linear access of…
A novel splitting algorithm is proposed for the numerical simulation of neuromorphic circuits. The algorithm is grounded in the operator-theoretic concept of monotonicity, which bears both physical and algorithmic significance. 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…
For computation, there existed Turing machine and later-matured automata theory. For low-level parallel computation, there existed variants of Turing machine, such as two-tapes Turing machine and multi-tapes Turing machine. In the…
Tree kernels are fundamental tools that have been leveraged in many applications, particularly those based on machine learning for Natural Language Processing tasks. In this paper, we devise a parallel implementation of the sequential…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
Presented here is an algorithm for a type-II quantum computer which simulates the Ising model in one and two dimensions. It is equivalent to the Metropolis Monte-Carlo method and takes advantage of quantum superposition for random number…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
A signal machine is an abstract geometrical model for computation, proposed as an extension to the one-dimensional cellular automata, in which discrete time and space of cellular automata is replaced with continuous time and space in signal…
We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is…
Optimally mapping a parallel application to compute and communication resources is increasingly important as both system size and heterogeneity increase. A similar mapping problem exists in gate-based quantum computing where the objective…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
A variant of Turing machines is introduced where the tape is replaced by a single tree which can be manipulated in a style akin to purely functional programming. This yields two benefits: first, the extra structure on the tape can be…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
We introduce a new type of generalized Turing machines (GTMs), which are intended as a tool for the mathematician who studies computability in Analysis. In a single tape cell a GTM can store a symbol, a real number, a continuous real…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
We improve the results by Siegelmann & Sontag (1995) by providing a novel and parsimonious constructive mapping between Turing Machines and Recurrent Artificial Neural Networks, based on recent developments of Nonlinear Dynamical Automata.…
The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access…
Parallel algorithms for solving any image processing task is a highly demanded approach in the modern world. Cellular Automata (CA) are the most common and simple models of parallel computation. So, CA has been successfully used in the…