On the invertible cellular automata 150 over Fp

In this work the reversibility problem for cellular automata with rule number 150 over the finite field F"p is tackled. It is shown that when null boundary conditions are stated, the reversibility is independent of the state set F"p and it appears when the number of cells of the cellular space satisfies some conditions. Furthermore, the explicit expressions of the inverse cellular automata are computed.

[1]  Jarkko Kari,et al.  Reversible Cellular Automata , 2005, Developments in Language Theory.

[2]  Pino Caballero-Gil,et al.  On the Use of Cellular Automata in Symmetric Cryptography , 2010, ArXiv.

[3]  Parimal Pal Chaudhuri,et al.  Theory and Applications of Cellular Automata in Cryptography , 1994, IEEE Trans. Computers.

[4]  Palash Sarkar,et al.  A brief history of cellular automata , 2000, CSUR.

[5]  Ángel Martín del Rey,et al.  Reversibility of linear cellular automata , 2011, Appl. Math. Comput..

[6]  Moawwad E. A. El-Mikkawy,et al.  A fast algorithm for evaluating n th order tri-diagonal determinants , 2004 .

[7]  Fumitaka Yura,et al.  On reversibility of cellular automata with periodic boundary conditions , 2004 .

[8]  G. Rodríguez Sánchez,et al.  On The Reversibility Of 150 Wolfram Cellular Automata , 2006 .

[9]  J. C. Mora.  Matrix methods and local properties of reversible one-dimensional cellular automata , 2002 .

[10]  Jarkko Kari,et al.  Theory of cellular automata: A survey , 2005, Theor. Comput. Sci..

[11]  Tim Boykett,et al.  Efficient exhaustive listings of reversible one dimensional cellular automata , 2004, Theor. Comput. Sci..

[12]  Hasan Akin,et al.  Reversibility of 1D Cellular Automata with Periodic Boundary over Finite Fields $\pmb{ {\mathbb{Z}}}_{p}$ , 2011 .

[13]  N. Margolus,et al.  Invertible cellular automata: a review , 1991 .

[14]  Eugen Czeizler.  On the size of the inverse neighborhoods for one-dimensional reversible cellular automata , 2004, Theor. Comput. Sci..

[15]  Hasan Akin,et al.  Characterization of two-dimensional cellular automata over ternary fields , 2011, J. Frankl. Inst..