Open AccessJournal Article
Universal Computation in Few-body Automata.
Reads0
Chats0
TLDR
This paper proves theorems describing the space, time, and state-set complexity of the simulation of d-dimensional conventional cellular automata with N-body automata, and shows that there exist computation-universal 2- body automata requiring 5.81 bits of state per cell.Abstract:
Few-body automata are a class of cellular automata. They were developed specifically to investigate the possibility of implementing a new generation of cellular automata machines that would use dense arrays of nanometer-scale device-cells. In this paper, we try to determine how many states per cell are required by few-body automata in order to perform universal computation. We prove theorems describing the space, time, and state-set complexity of the simulation of d-dimensional conventional cellular automata with N-body automata, and show that there exist computation-universal 2-body automata requiring 5.81 bits of state per cell for d = 1 and 2 bits per cell for d = 2. These results suggest that physically-imposed restrictions on the number of available bits per cell will not be an obstacle to cellular automaton-like computation at nanometer scales.read more
Citations
More filters
Proceedings ArticleDOI
Algorithmic Self-Assembly of DNA
TL;DR: In this paper, the authors focus on molecular self-assembly, giving examples of engineered DNA tiles that crystallize into two-dimensional sheets, one-dimensional tubes and ribbons, and information-guided patterns such as a Sierpinski triangle and a binary counter.
Simulations of Computing by Self-Assembly
TL;DR: In this article, the authors developed a more realistic model based on the thermodynamics and kinetics of oligonucleotide hydridization, and investigated what physical factors influence the error rates.
Proceedings ArticleDOI
Can quantum computers have simple Hamiltonians
TL;DR: The quantum cellular automata can be described by relatively simple Hamiltonians that resemble the Hamiltonians of spin systems as mentioned in this paper, and the one-dimensional XY Hamiltonian is exactly solvable.
References
More filters
Book
Computation: Finite and Infinite Machines
TL;DR: In this article, the authors present an abstract theory that categorically and systematically describes what all these machines can do and what they cannot do, giving sound theoretical or practical grounds for each judgment, and the abstract theory tells us in no uncertain terms that the machines' potential range is enormous and that its theoretical limitations are of the subtlest and most elusive sort.
Journal ArticleDOI
Quantum Mechanical Computers
TL;DR: The physical limitations due to quantum mechanics on the functioning of computers are analyzed in this paper, where the physical limitations of quantum mechanics are discussed and the physical limits of quantum computing are analyzed.
Universality and complexity in cellular automata
TL;DR: In this article, it was shown that all one-dimensional cellular automata fall into four distinct universality classes: limit points, limit cycles, chaotic attractors, and limit cycles.
Journal ArticleDOI
Universality and complexity in cellular automata
TL;DR: Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes, and one class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.