Some algorithms for real-time generation of non-regular sequences on one-bit inter-cell-communication cellular automata

Kamikawa, Naoki; Umeo, Hiroshi

doi:10.1109/sice.2007.4421122

Cited by 9 publications

(15 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most of the generation algorithms proposed so far in Arisawa [5], Fischer [6], Korec [7], Umeo and Kamikawa [8], [9], and Kamikawa and Umeo [10]- [12] are based on geometric properties in the time-space domain with interactions of fixed-speed signals. This section presents an interesting example of a non-regular sequence generated by a - - Table 5 A list of non-regular sequences generated by two-state CAs.…”

Section: Generation Algorithm For Sequencementioning

confidence: 99%

“….} were designed by Arisawa [5] and Kamikawa and Umeo [11]. Arisawa [5] showed that the sequence {2 n | n = 1, 2, 3, .…”

Section: Generation Algorithms For Three-state Camentioning

confidence: 99%

“…Arisawa's algorithms aren't optimal in generation time. Kamikawa and Umeo [11] showed that the sequence {2 n | n = 1, 2, 3, . .…”

Section: Generation Algorithms For Three-state Camentioning

confidence: 99%

“…On the other hand, Arisawa [5], Fischer [6], Korec [7], Umeo and Kamikawa [8], [9], and Kamikawa and Umeo [10]- [12] studied a similar sequence generation problem in different settings, where a leftmost cell of the array generates a state sequence indicated by an internal state set. The time series in which the leftmost cell falls into a special designated state as the sequence generated by the CA is described.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Study on Sequence Generation Powers of Small Cellular Automata

Kamikawa

Umeo

2012

SICE Journal of Control, Measurement, and System Integration

View full text Add to dashboard Cite

A model of cellular automata (CA) is considered to be a well-studied non-linear model of complex systems in which an infinite one-dimensional array of finite state machines (cells) updates itself in a synchronous manner according to a uniform local rule. A sequence generation problem on the CAs has been studied and many scholars proposed several real-time sequence generation algorithms for a variety of non-regular sequences such as prime, Fibonacci, and {2 n | n = 1, 2, 3, . . .} sequences etc. The paper describes the sequence generation powers of CAs having a small number of states, focusing on the CAs with one, two, and three internal states, respectively. The authors enumerate all of the sequences generated by two-state CAs and present several non-regular sequences that can be generated in real-time by three-state CAs, but not generated by any two-state CA. It is shown that there exists a sequence generation gap among the powers of those small CAs.as the authors know, no work, except for this paper, has been done concerning the study of generation powers of CAs with a small number of states.This paper extends the study of Kamikawa and Umeo [12] exhaustively, study sequence generation powers of CAs with a small number of states, and give formal proofs of all algorithms presented. The sequence generation powers of small CAs, focusing on the CAs with one, two, and three internal states is investigeted. The authors enumerate all of the sequences generated by two-state CAs and present several non-regular sequences that can be generated in real-time by three-state CAs, but not generated by any two-state CAs. It is shown that there exists a sequence generation gap among the powers of those small CAs.

show abstract

Section: Generation Algorithm For Sequencementioning

confidence: 99%

“….} were designed by Arisawa [5] and Kamikawa and Umeo [11]. Arisawa [5] showed that the sequence {2 n | n = 1, 2, 3, .…”

Section: Generation Algorithms For Three-state Camentioning

confidence: 99%

“…Arisawa's algorithms aren't optimal in generation time. Kamikawa and Umeo [11] showed that the sequence {2 n | n = 1, 2, 3, . .…”

Section: Generation Algorithms For Three-state Camentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Study on Sequence Generation Powers of Small Cellular Automata

Kamikawa

Umeo

2012

SICE Journal of Control, Measurement, and System Integration

View full text Add to dashboard Cite

show abstract

“…A sequence generation problem is one of the major topics in the application of CAs. Arisawa [1], Fischer [2], Korec [10], and Kamikawa and Umeo [3][4][5][6][7][8] studied the sequence generation problem, where a leftmost cell of the array generates an infinite non-regular sequence indicated by an internal state set. In those studies, much attention has been paid to the developments of real-time generation algorithms and their small-state implementations on CAs for specific non-regular sequences.…”

Section: Introductionmentioning

confidence: 99%

Two Implementations of Real-Time Sequence Generator for {n<sup>3</sup> | n=1, 2, 3, ... } and Their Comparison

Kamikawa

Umeo

2019

IJNC

View full text Add to dashboard Cite

A cellular automaton (CA) is a well-studied non-linear computational model of complex systems in which an infinite one-dimensional array of finite state machines (cells) updates itself in a synchronous manner according to a uniform local rule. A sequence generation problem on the CA model has been studied for a long time and a lot of generation algorithms has been proposed for a variety of non-regular sequences such as {2 n | n = 1, 2, 3,. . .}, prime, and Fibonacci sequences etc. In this paper, we study a real-time sequence generator for {n 3 | n = 1, 2, 3,. . .}. In the previous studies, Kamikawa and Umeo(2018) showed that sequence {n 3 | n = 1, 2, 3,. . .} can be generated in real-time by an eight-state CA. We present a new six-state implementation of real-time sequence generator for {n 3 | n = 1, 2, 3,. . .} rather than reducing the internal state of the Kamikawa and Umeo's sequence generator and give a formal proof of the correctness of the generator. In addition, we show the number of state-changes and number of cells of sequence generators, and compare sequence generators.

show abstract

Millions of 5-State $$n^3$$-Real Time Sequence Generators via Local Simulations

Nguyen

Maignan

2022

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Some algorithms for real-time generation of non-regular sequences on one-bit inter-cell-communication cellular automata

Cited by 9 publications

References 3 publications

A Study on Sequence Generation Powers of Small Cellular Automata

A Study on Sequence Generation Powers of Small Cellular Automata

Two Implementations of Real-Time Sequence Generator for {n<sup>3</sup> | n=1, 2, 3, ... } and Their Comparison

Millions of 5-State $$n^3$$-Real Time Sequence Generators via Local Simulations

Contact Info

Product

Resources

About