## Computing Shifts in 90/150 Cellular Automata Sequences (2001)

Venue: | Applications, Volume 9, Issue |

Citations: | 3 - 1 self |

### BibTeX

@ARTICLE{Sarkar01computingshifts,

author = {Palash Sarkar},

title = {Computing Shifts in 90/150 Cellular Automata Sequences},

journal = {Applications, Volume 9, Issue},

year = {2001},

volume = {2},

pages = {175--186}

}

### OpenURL

### Abstract

Sequences produced by cellular automata (CA) are studied algebraically. A suitable k-cell 90/150 CA over F q generates a sequence of length q k 1. The temporal sequence of any cell of such a CA can be obtained by shifting the temporal sequence of any other cell. We obtain a general algorithm to compute these relative shifts. This is achieved by developing the proper algebraic framework for the study of CA sequences. 1

### Citations

214 |
Statistical mechanics of cellular automata
- Wolfram
- 1983
(Show Context)
Citation Context ...assume l i = u j = 1 for all 2 i n and 1 j n 1. Then the matrix M becomes a tridiagonal matrix with both the lower and upper sub diagonal equal to 1. If q = 2, such a CA is called a 90/150 CA [9]. Following this convention we will call such a CA a 90/150 CA, even if q > 2. Interestingly, for 90/150 CA and q = 2, the set of strings a 1 : : : a n which makes the matrix M non singular turns out ... |

48 | A Brief History of Cellular Automata
- Sarkar
- 2000
(Show Context)
Citation Context ...e that the transition rule can be dierent for dierent cells. This is usually required in VLSI applications of CA. The more usual model for CA assumes the same transition rule for all the cells. See [6] for a recent survey of the general theory of CA. The evolution of the state vector C t can be described as C t = MC t 1 ; t 1; (3) where M is the matrix dened in Equation (1). The matrix M is call... |

11 | Introduction to and their applications - Lidl, Niederreiter - 1986 |

8 |
Continued fraction expansions of rational expressions with irreducible denominators in characteristic 2
- Mesirov, Sweet
- 1987
(Show Context)
Citation Context ... Remarks When q = 2, it is possible to obtain the string a 1 : : : a k from the polynomial f(x). An algorithm to do this was described by Tezuka and Fushimi [8] based on a result by Mesirov and Sweet =-=[5]-=-. Given a degree k irreducible polynomial f(x) over F 2 , there are at most 2 distinct k-cell CA whose characteristic polynomial is f(x). The two CA are described by either the string a 1 : : : a k or... |

8 |
A method of designing cellular automata as pseudorandom number generators for built-in self-test for VLSI
- Tezuka, Fushimi
- 1994
(Show Context)
Citation Context ...ge space required is O(kq k ). 6 Concluding Remarks When q = 2, it is possible to obtain the string a 1 : : : a k from the polynomial f(x). An algorithm to do this was described by Tezuka and Fushimi =-=[8]-=- based on a result by Mesirov and Sweet [5]. Given a degree k irreducible polynomial f(x) over F 2 , there are at most 2 distinct k-cell CA whose characteristic polynomial is f(x). The two CA are desc... |

5 |
Orthogonal sequences of polynomials over arbitrary fields
- Blackburn
- 1998
(Show Context)
Citation Context ...ory was provided in [1]. To the best of our knowledge, no CA design algorithm is known for q > 2. This question is connected to the orthogonal multiplicity of polynomials inselds F q with q 6= 2 (see =-=[3]-=-). Computational results from [3] suggest that for each degree k primitive polynomial f(x) over F q it is possible to construct a CA whose characteristic polynomial is f(x). It is not clear that such ... |

3 |
The set of reversible 90/150 cellular automata is regular
- Sarkar, Barua
- 1998
(Show Context)
Citation Context ...on we will call such a CA a 90/150 CA, even if q > 2. Interestingly, for 90/150 CA and q = 2, the set of strings a 1 : : : a n which makes the matrix M non singular turns out to be a regular set. See =-=[7] for -=-a proof of this fact and also an exact enumeration of the set of such \reversible" strings. Theorem 3.2 Let C be a k-cell 90/150 CA over F q having STM M . Then the minimal polynomial of M is equ... |

1 |
Analysis of cellular automata used as pesudorandom pattern generators
- Bardell
- 1990
(Show Context)
Citation Context ...tes the problem of studying the relative shift between the sequences C t i and C t j for 1 is k. This problem is equivalent to the problem dened before. The problem was earlier studied by Bardell [1]. In [1], an operational method to compute the shifts for a 6-cell CA was described. However, no algebraic justication or general algorithm was provided in [1]. In this paper, we approach the study o... |

1 |
personal communication
- Barua
(Show Context)
Citation Context .... Since f(M) = 0 (by Cayley-Hamilton theorem), this means M i I k = 0. Since ord(M) = q k 1, we have i = q k 1. Hence f(x) is primitive. if : (This proof has been conveyed to the author by Rana Barua =-=[2-=-].) For any non zero v 2 F k q , dene fv (x), the minimal polynomial for v, to be the least degree monic polynomial such that fv (M)v = 0. An easy application of the division algorithm shows that fv (... |