Related papers: Multiway Turing Machines
We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. Such a problem relates to recent developments in copula modeling for discrete random vectors.…
Configurable arrays of optically trapped Rydberg atoms are a versatile platform for quantum computation and quantum simulation, also allowing controllable decoherence. We demonstrate theoretically, that they also enable proof-of-principle…
A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off…
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these…
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…
Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model,…
Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to…
Articulated multi-axle vehicles are interesting from a control-theoretic perspective due to their peculiar kinematic offtracking characteristics, instability modes, and singularities. Holonomic and nonholonomic constraints affecting the…
Multi-stack machines and Turing machines can simulate to each other. In this note, we give a succinct definition of multi-stack machines, and from this definition it is clearly seen that pushdown automata and deterministic finite automata…
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…
We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a…
We prove the following facts about the language recognition power of quantum Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more powerful than probabilistic Turing machines for any common space bound $ s $…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…
Interface theories are powerful frameworks supporting incremental and compositional design of systems through refinements and constructs for conjunction, and parallel composition. In this report we present a first Interface Theor -- |Modal…
The task of classifying the entanglement properties of a multipartite quantum state poses a remarkable challenge due to the exponentially increasing number of ways in which quantum systems can share quantum correlations. Tackling such…
Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical…
Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…
As was well known, in classical computation, Turing machines, circuits, multi-stack machines, and multi-counter machines are equivalent, that is, they can simulate each other in polynomial time. In quantum computation, Yao [11] first proved…
Multiple extensions of Recurrent Neural Networks (RNNs) have been proposed recently to address the difficulty of storing information over long time periods. In this paper, we experiment with the capacity of Neural Turing Machines (NTMs) to…