The reversibility problem for a family of two-dimensional cellular automata

Mehmet Emin KÖROĞLU; İrfan ŞİAP; Hasan AKIN

Makale detayları

The reversibility problem for a family of two-dimensional cellular automata

Yazarlar:

Mehmet Emin KÖROĞLU | İrfan ŞİAP | Hasan AKIN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2016 Vol.40 Issue 3, pp.665-678

Belge Tipi:

Makale

Yayın Tarihi:

5/2016

Belge Dili:

Türkçe

Document ID (Org No.):

2000746994

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

In this paper the reversibility problem of a family of two-dimensional cellular automata is completely resolved. It is well known that the reversibility problem is a very difficult one in general. In order to determine whether  a cellular automaton is reversible or not the reversibility of its rule matrix is studied via linear algebraic tools. However, in this particular study the authors consider a novel approach. By observing the algebraic structures of  rule matrices that represent these families and associating them with polynomials in two variables in a quotient ring, the solution to the reversibility problem is simplified greatly.  Hence, this approach not only drastically decreases the computational time for determining the reversibility of these families  but also provides an explicit construction of reverse cellular automata in the case of the existence of their inverses. The paper concludes with a consideration  of the rule matrices of these families in obtaining linear codes over group rings, which are referred to as zero-divisor codes.

Makale detayları

The reversibility problem for a family of two-dimensional cellular automata

Yazarlar: Mehmet Emin KÖROĞLU | İrfan ŞİAP | Hasan AKIN

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2016 Vol.40 Issue 3, pp.665-678

Belge Tipi: Makale

Yayın Tarihi: 5/2016

Belge Dili: Türkçe

Document ID (Org No.): 2000746994

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Mehmet Emin KÖROĞLU | İrfan ŞİAP | Hasan AKIN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2016 Vol.40 Issue 3, pp.665-678

Belge Tipi:

Makale

Yayın Tarihi:

5/2016

Belge Dili:

Türkçe

Document ID (Org No.):

2000746994

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098