scispace - formally typeset
Search or ask a question
Topic

Continuous automaton

About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, an integrable cellular automaton called the box-ball system (BBS) was derived directly from the integrably differential difference equation by either ultradiscretization or crystallization.
Abstract: We study an integrable cellular automaton which is called the box-ball system (BBS). The BBS can be derived directly from the integrable differential-difference equation by either ultradiscretization or crystallization. We clarify the integrable structure and the hidden symmetry of the BBS.

1 citations

Posted Content
13 Nov 2006
TL;DR: A new mathematical and systematic method stemming from the local very nature of any differential problem is proposed: a custom tailored continuous automaton is purposely derived from any given differential problem so that its steady state yields the solution in a quantitatively correct way.
Abstract: This paper presents an original and generic numerical method for solving partial differential equations. A new mathematical and systematic method stemming from the local very nature of any differential problem is proposed: a custom tailored continuous automaton is purposely derived from any given differential problem so that its steady state yields the solution in a quantitatively correct way. The combined use of formal computing and continuous automata thus offers the unique possibility to completely automate the process from formal problem specification to its numerical solution.

1 citations

Book ChapterDOI
01 Jan 2003
TL;DR: This chapter describes the cellular automaton model applications for bacterial pattern formation and avascular tumor growth and can easily be adapted to gain theoretical insight into the behavior of a wide range of other biological systems.
Abstract: Publisher Summary This chapter describes the cellular automaton model applications for bacterial pattern formation and avascular tumor growth. Principles underlying the dynamics of interacting cell systems can be analyzed by means of mathematical models. Cellular automata are discrete dynamical systems and provide a cell-based modelling alternative, in which the fate of individual cells can be tracked. Automaton configurations are updated synchronously or asynchronously, and they depend only on the local neighborhood configuration. The essential question is how macroscopic behavior can arise from individual rules. Cellular automata have become paradigms of self-organizing complex systems, in which collective behavior arises from simple interaction rules of even more simple components. An important insight of complex system research is that macroscopic behavior is rather independent of the precise choice of the microscopic interaction. Finally, the models introduced for the case of bacterial and tumor pattern formation can easily be adapted to gain theoretical insight into the behavior of a wide range of other biological systems.

1 citations

Book ChapterDOI
01 Jun 2008
TL;DR: Given a shift subspace over a finitely generated group, the subshift induced by it on a larger group is defined and the old automaton inside the new one is simulated, and some consequences and restrictions are discussed.
Abstract: Given a shift subspace over a finitely generated group, we define the subshift induced by it on a larger group. Then we do the same with cellular automata and, while observing that the new automaton can model a different abstract dynamics, we remark several properties that are shared with the old one. After that, we simulate the old automaton inside the new one, and discuss some consequences and restrictions.

1 citations

Proceedings ArticleDOI
TL;DR: In this paper, a stochastic, linear, S-model automaton model is proposed for distributed adaptive routing in packet-switched datagram networks and the performance of two automata-based adaptive routing algorithms is compared.
Abstract: Large computer networks with dynamic links present special problems in adaptive routing. If the rate of change in the network links is fairly rapid and the changes are nonperiodic, then obtaining the optimal solution for adaptive routing becomes complex and expensive. In addition to the academic value of the solution, the growth of computer networks gives the problem practical importance. Learning automata is logical approach to the above problem. With the right parameter values, learning automata can converge arbitrarily close to the solution for a given network topology and set of conditions. The adaptability of automata reduces the depth of analysis needed for network behavior; the survivability and robustness of the network is also enhanced. Finally, each automaton behaves independently, making automata ideal for distributed decision-making, and minimizing the need for inter-node communication. Previous work on automata and network routing do not address how changes in network parameter values affect the performance of automata-based adaptive routing. Such knowledge is essential if we are to determine the suitability of an automata-based routing algorithm for a given network. Our paper focuses on this question and shows that in packet- switched datagram networks, relationships do indeed exist between network parameters and the performance of distributed adaptive routing algorithms. Additionally, our paper compares the performance and behavior of several types of learning automata, as well as changes in automata behavior over a range of reward and penalty values. Finally, the performance of two automata-based adaptive routing algorithms is compared. Our automaton model is a stochastic, linear, S-model automaton. In other words, the automaton's matrix of action probabilities changes as a result of performance feedback which it receives from the environment, the response to environment feedback is linear, and finally, the feedback it receives from the environment is over a continuous interval.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

1 citations

Network Information
Related Topics (5)
Time complexity
36K papers, 879.5K citations
81% related
Graph (abstract data type)
69.9K papers, 1.2M citations
77% related
Approximation algorithm
23.9K papers, 654.3K citations
77% related
Graph theory
20.8K papers, 691.4K citations
76% related
Computational complexity theory
30.8K papers, 711.2K citations
76% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
202219
20212
20192
20184
201719