Fig 4 - uploaded by Nobuyuki Matsui
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Decoding construction signals into corresponding constructions. (i) If a forward construction signal arrives at the end of an arm, it makes the arm move one cell; similarly, (ii) a left-turn and (iii) a right-turn construction signals bend the arm leftward and rightward, respectively.
Source publication
This paper proposes a universal constructor implemented on a self-timed cellular automaton, which is a particular type of asynchronous cellular automaton. Our construction utilizes the asynchronous nature of the underlying cellular automaton in a direct way, as a result of which it is simpler than the conventional construction based on the simulati...
Contexts in source publication
Context 1
... a construction signal arrives at the end of a construction arm (3-0), it is decoded and executed to extend the arm one cell forward, to the left, or right cor- respondingly, according to the contents of the construction signal (see Fig. 4). After the trace signal completes encoding the entire shape, it arrives at the T-conjunction. Then, self-reproduction enters into the second stage, that is, verifying whether a new child loop is formed. The trace signal pads at the T-conjunction pro- duces a validation signal (2-2). Its arrival at the end of construction arm indicates ...
Context 2
... situations. This method follows the ¯rst-in-last-out principle. That is, arms that collide with other blocked arm, should withdraw ¯rst. Only after those arms collided on a arm have begun to withdraw, can the blocked arm withdraw. To describe our disentanglement method clearly, Fig. 13 shows the entanglement of four arms. Correspondingly, Fig. 14 shows the simulations of the disentangled processes in Fig. 13, as carried out in our simulator. To verify our proposed disentanglement method further, Fig. 15 provides an example of more intense collisions among about 50 di®erent twisted arms. After 10 steps, these arms can be disentangled successfully. Furthermore, the numerical ...
Context 3
... the numerical simulations on these 50 arms in Fig. 16 show the average withdrawal time and variance of each arm under 50 di®erent experiments. 1 and 4 entangle together to form a \circle," and four collision points are generated labeled 1À4. Any one arm in this \circle" that ¯rst withdraws can make the arm that collides with it withdraw without blocking, and the \circle" is unfastened. ...
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Citations
... Peper et al. implemented DI circuits using only 9 and 6 transition rules, respectively, in [28] and [29], on self-timed CAs (STCAs) [16,28], a particular type of ACAs, in which the state of each cell is partitioned like in PCAs. STCAs have also been used to implement universal construction by Takada et al. [30,31]. Though STCAs tend to allow implementations requiring few transition rules, they suffer from their inability to have neighboring cells undergo transitions simultaneously. ...
... Furthermore, unlike conventional models of CAs such as Codd's [2], their cell states are not strongly symmetric, i.e., rotating a cell gives strictly speaking a different cell state. Due to this, STCAs tend to use more cell states than ACAs implementing the same functionality (e.g., 2 8 = 256 states are required in [30,31]). ...
... In this paper, we propose a computation-and construction-universal ACA with von Neumann neighborhood, and show how it can be used to implement self-reproducing machines. Our model employs strongly symmetric cells with 15 states and allows purely asynchronous updating, in contrast to the construction-universal STCA in [30,31]. ...
Universality in cellular automata (CAs), first studied by von Neumann, has attracted much research efforts over the years, especially for CA employing synchronous timing. This paper proposes a computation- and construction-universal CA with a von Neumann neighborhood that is updated in a purely asynchronous way, rather than by the conventional but less efficient way of simulating synchronous CAs on asynchronous CAs. The proposed asynchronous CA is capable of implementing self-reproducing machines. Our model employs strongly symmetric cells with 15 states.
... An example is Morita and Imai's study of self-replication in the context of reversible cellular automata [15] (in a reversible CA, every configuration has at most one predecessor), inspired by reversible logic in digital circuits. Similarly, Peper et al. [16] [17] have developed selfreplicating structures in Self-Timed Cellular Automata (STCA). This kind of automata do not rely on a global synchronization mechanism to update the states of the cells, but rather the state transitions only occur when triggered by transitions in neighboring cells. ...
This article presents the implementation of a self-replication algorithm in a Field Programmable Gate Array (FPGA). Whereas previous research on self-replication has been mostly limited to theoretical examples and small problem sizes, this work shows how the Tom Thumb self-replication algorithm can be extended to take into account realistic FPGA architectures and representative processor-scale digital logic circuits. To achieve this objective, the algorithm was implemented within the POEtic tissue, a programmable logic device for bio-inspired systems, and a dedicated processor, based on the MOVE paradigm, was developed. Starting from a single processor, the self-replication process can be used to generate an arbitrarily large array of identical processors that then differentiate to realize a given application. In this article, this process is demon-strated through a four-processor system that implements a simple counter. The ultimate goal of this research is to demonstrate how a bio-inspired approach can exploit self-replication to tackle the complexity and high fault rates of next-generation electronic devices.
This paper presents a novel scheme to construct circuits on the cell space of an asynchronous cellular automaton that has partitioned cells. The construction process in this scheme is conducted by worm configurations that contain instructions on how to operate. Circuits are constructed by multiple worms, which move around in parallel on the cell space, resulting in an efficient process, as is shown.
Self-reproduction is one of the basic characteristics in nature. Since biological systems are abundant in indeterminism, it thus makes sense to model systems in nature under asynchronous timing mode. With this in mind, this paper proposes a novel triggered reproduction of self-reproduction loops (SRLs) on self-timed cellular automaton (STCA), a type of asynchronous cellular automaton (ACA). SRLs in our self-reproduction model are triggered one by one to perform self-reproduction, which implies only one SRL is engaged in self-reproduction at one time. Moreover, collisions caused by interplays between SRLs can be transformed into triggering the new round self-reproduction of the collided loop, avoiding unpredictable interplays rooted in ACA. Experiment verifies the validity of the triggered self-reproductive model.
Self-reproduction on asynchronous cellular automata (ACAs) has attracted
wide attention due to the evident artifacts induced by synchronous
updating. Asynchronous updating, which allows cells to undergo
transitions independently at random times, might be more compatible with
the natural processes occurring at micro-scale, but the dark side of the
coin is the increment in the complexity of an ACA in order to accomplish
stable self-reproduction. This paper proposes a novel model of
self-timed cellular automata (STCAs), a special type of ACAs, where
unsheathed loops are able to duplicate themselves reliably in parallel.
The removal of sheath cannot only allow various loops with more flexible
and compact structures to replicate themselves, but also reduce the
number of cell states of the STCA as compared to the previous model
adopting sheathed loops [Y. Takada, T. Isokawa, F. Peper and N. Matsui,
Physica D227, 26 (2007)]. The lack of sheath, on the other hand, often
tends to cause much more complicated interactions among loops, when all
of them struggle independently to stretch out their constructing arms at
the same time. In particular, such intense collisions may even cause the
emergence of a mess of twisted constructing arms in the cellular space.
By using a simple and natural method, our self-reproducing loops (SRLs)
are able to retract their arms successively, thereby disentangling from
the mess successfully.
Definition of the SubjectMachine self-replication, besides inspiring numerous fictional books and movies, has long been considered a powerful paradigm to allow artifacts, for example, to survive in hostile environments (such as other planets) or to operate more efficiently by creating populations of machines working together to achieve a given task. Where the self-replication of computing machines is concerned, other motivations can also come into play, related to concepts such as fault tolerance and self-organization.Cellular automata have traditionally been the framework of choice for the study of self-replicating computing machines, ever since they were used by John von Neumann, who pioneered the field in the 1950s. In this context, self-replication is seen as the process whereby a configuration in the cellular space is capable of creating a copy of itself in a di ...
Molecular-scale integrated circuits will provide hardware de- signers with astounding computational resources. However, current design methodologies—which already struggle to ex- ploit the resources available today—are ill-suited to the com- plexity and high fault rates of these novel technologies. Nature, on the other hand, has evolved ways of coping with these issues. A human being consists of approximately 60 trillion (60 ◊ 1012) cells, ceaselessly operating throughout the lifetime of the organ- ism. Faults occur at a very high rate, but (in the majority of cases) are successfully detected and repaired with little or no effect on the organism. It is therefore legitimate to wonder if it is possible to draw inspiration from nature to find ways to cope with the complexity of molecular-scale electronics. One of the basic mechanisms behind the resilience of biolog- ical organisms is cellular division, i.e., the ability of the cells to self-replicate. Indeed the idea of self-replicating computing ma- chines has a long history, starting in the 1950s with the semi- nal work of John von Neumann1 and continuing in the 1980s with the research of Chris Langton.2 More recently, the predicted features of nanoelectronic devices have sparked a renewed inter- est in the topic.3-6 Our own research7-10 addresses the develop- ment of self-replication approaches that can be integrated within complex digital systems able to operate in the presence of faulty components.
This paper proposes self-reproducing loops (SRLs) implemented on a self-timed cellular automaton (STCA), a type of asynchronous cellular automaton (ACA). Self-reproduction of a wide variety of shapes of SRLs is made possible by employing the so-called shape-encoding mechanism, which self-inspects a loop and generates construction signals accordingly. Due to the model’s asynchronous mode of timing, a dynamic interplay between SRLs occurs, in which SRLs compete for space to place their offspring. Deadlock situations caused by the collisions are reliably arbitrated utilizing only local interactions of SRLs.
