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Computing with Solitons: A Review and Prospectus
"... We review work on computing with solitons, from the discovery of solitons in cellular automata, to an abstract model for particle computation (particle machines), to information transfer in collisions of (continuum) optical solitons, to state transformations in collisions of Manakov (vector) soliton ..."
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Cited by 14 (1 self)
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We review work on computing with solitons, from the discovery of solitons in cellular automata, to an abstract model for particle computation (particle machines), to information transfer in collisions of (continuum) optical solitons, to state transformations in collisions of Manakov (vector) solitons. We conclude by discussing open problems and the prospects for practical applications using optical solitons in photorefractive crystals and other materials. 1
Computation by asynchronously updating cellular automata
 Journal of Statistical Physics
, 2004
"... Abstract. A known method to compute on an asynchronously updating cellular automaton is the simulation of a synchronous computing model on it. Such a scheme requires not only an increased number of cell states, but also the simulation of a global synchronization mechanism. Asynchronous systems tend ..."
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Cited by 12 (4 self)
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Abstract. A known method to compute on an asynchronously updating cellular automaton is the simulation of a synchronous computing model on it. Such a scheme requires not only an increased number of cell states, but also the simulation of a global synchronization mechanism. Asynchronous systems tend to use synchronization only on a local scale—if they use it at all. Research on cellular automata that are truly asynchronous has been limited mostly to trivial phenomena, leaving issues such as computation unexplored. This paper presents an asynchronously updating cellular automaton that conducts computation without relying on a simulated global synchronization mechanism. The 2dimensional cellular automaton employs a Mooreneighborhood and 85 totalistic transition rules describing the asynchronous interactions between the cells. Despite the probabilistic nature of asynchronous updating, the outcome of the dynamics is deterministic. This is achieved by simulating delay insensitive circuits on it, a type of asynchronous circuit that is known for its robustness to variations in the timing of signals. We implement three primitive operators on the cellular automaton from which any arbitrary delay insensitive circuit can be constructed, and show how to connect the operators such that collisions of crossing signals are avoided.
Reversible Cellular Automaton Able to Simulate Any Other Reversible One Using Partitioning Automata
, 1995
"... Partitioning automata (PA) are defined. They are equivalent to cellular automata (CA). Reversible subclasses are also equivalent. A simple, reversible and universal partitioning automaton is described. Finally, it is shown that there are reversible PA and CA that are able to simulate any reversible ..."
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Cited by 7 (5 self)
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Partitioning automata (PA) are defined. They are equivalent to cellular automata (CA). Reversible subclasses are also equivalent. A simple, reversible and universal partitioning automaton is described. Finally, it is shown that there are reversible PA and CA that are able to simulate any reversible PA or CA on any configuration.
Cellular Automata and Artificial Life  Computation and Life in Reversible Cellular Automata 
 in Complex Systems, E. Goles and
, 1998
"... In this paper, we investigate and discuss the problem how the abilities of computing and selfreproduction can be realized in a "reversible" environment, especially in reversible cellular automata (RCA). An RCA is a "backward deterministic" CA in which every configuration of the ..."
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Cited by 3 (0 self)
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In this paper, we investigate and discuss the problem how the abilities of computing and selfreproduction can be realized in a "reversible" environment, especially in reversible cellular automata (RCA). An RCA is a "backward deterministic" CA in which every configuration of the cellular space has at most one predecessor. Such systems have a close connection to physical reversibility, and have been known to play an important role in the problem of inevitable power dissipation in computing systems. This problem will become much more important when one tries to construct nanoscaled functional objects based on microscopic physical law. We first discuss how computationuniversality can be obtained under the reversibility constraint, and show our models of one and twodimensional universal RCAs. Next, we explain a selfreproducing model on a twodimensional RCA and its mechanism. Our new attempt of creating a threedimensional selfreproducing RCA is also stated. 1 Introduction Cellular ...
Katsunobu IMAI †,Yousuke KASAI †,Yuya SONOYAMA ‡,
"... Selfreproduction and shape formation in two and three dimensional cellular ..."
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Selfreproduction and shape formation in two and three dimensional cellular
Information Sciences xxx (2012) xxx–xxx Contents lists available at SciVerse ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins
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www.elsevier.com/locate/jcss Delayinsensitive computation in asynchronous cellular automata
, 2004
"... Asynchronous cellular automata (ACA) are cellular automata that allow cells to update their states independently at random times. Because of the unpredictability of the order of update, computing on ACA is usually done by simulating a timing mechanism to force all cells into synchronicity after whic ..."
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Asynchronous cellular automata (ACA) are cellular automata that allow cells to update their states independently at random times. Because of the unpredictability of the order of update, computing on ACA is usually done by simulating a timing mechanism to force all cells into synchronicity after which wellestablished synchronous methods of computation can be used. In this paper, we present a more effective method of computation based upon a 4state twodimensional ACA with von Neumann neighborhood that is based on the construction in the cellular space of delayinsensitive circuits, a special type of asynchronous circuits, whose operations are robust to arbitrary delays in operators or interconnection lines. We show that this novel ACA model can be used to construct a universal Turing machine, which suffices to prove its computational universality.
Short title: Laying Out Circuits on Asynchronous Cellular Arrays Laying Out Circuits on Asynchronous Cellular Arrays: A step towards Feasible Nanocomputers?
"... Opinions differ widely as to the type of architectures most suitable for achieving the tremendous performance gains expected with computers built by nanotechnology. In this context few research efforts have gone to asynchronous cellular arrays, an architecture that is promising for nanocomputers due ..."
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Opinions differ widely as to the type of architectures most suitable for achieving the tremendous performance gains expected with computers built by nanotechnology. In this context few research efforts have gone to asynchronous cellular arrays, an architecture that is promising for nanocomputers due to 1. its regular structure of locally interconnected cells, and 2. its asynchronous mode of timing. The first facilitates bottomup manufacturing techniques like directed selfassembly. The second allows the cells ’ operations to be timed randomly and independently of each other, mitigating the problems accompanying a central clock, like high power consumption and heat dissipation. The advantages of asynchronous timing notwithstanding, it makes computation less straightforward. Attempts to compute on asynchronous cellular arrays have therefore focused on simulating synchronous operation on them, at the price of more complex cells. Here we advance a more effective approach based on the configuration on an asynchronous cellular array of delayinsensitive circuits, a type of asynchronous circuits that is robust to arbitrary delays in signals. Our results may be a step towards future nanocomputers with a huge number of autonomously operating cells organized in homogeneous arrays that can be programmed by configuring them as delayinsensitive circuits. 1.