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Kevin Cattell, Jon C. Muzio, "Analysis of OneDimensional Linear Hybrid Cellular Automata over GF(q)," IEEE Transactions on Computers, vol. 45, no. 7, pp. 782792, July, 1996.  
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@article{ 10.1109/12.508317, author = {Kevin Cattell and Jon C. Muzio}, title = {Analysis of OneDimensional Linear Hybrid Cellular Automata over GF(q)}, journal ={IEEE Transactions on Computers}, volume = {45}, number = {7}, issn = {00189340}, year = {1996}, pages = {782792}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.508317}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Analysis of OneDimensional Linear Hybrid Cellular Automata over GF(q) IS  7 SN  00189340 SP782 EP792 EPD  782792 A1  Kevin Cattell, A1  Jon C. Muzio, PY  1996 KW  Cellular automata KW  characteristic polynomial KW  finite field KW  LFSM. VL  45 JA  IEEE Transactions on Computers ER   
Abstract—This paper studies theoretical aspects of onedimensional linear hybrid cellular automata over a finite (Galois) field. General results concerning the characteristic polynomials of such automata are presented. A probabilistic synthesis algorithm for determining such a linear hybrid cellular automaton with a specific characteristic polynomial is given, along with empirical results and a theoretical analysis. Cyclicboundary cellular automata are defined and related to the more common nullboundary cellular automata. An explicit similarity transform between a cellular automaton and its corresponding linear feedback shift register is derived.
[1] P.H. Bardell, Analysis of Cellular Automata Used as a PseudoRandom Pattern Generators Proc. Int'l Test Conf., pp. 762768, 1990.
[2] D. Roy Chowdhury, S. Basu, I. Sen Gupta, and P. Pal Chaudhuri, "Design of CAECC—Cellular Automata Based Error Correcting code," IEEE Trans. Computers, vol. 43, no. 6, pp. 759764, June 1994.
[3] A. Das and P.P. Chaudhuri, “PseudoExhaustive Test Pattern Generation Using Cellular Automata,” IEEE Trans. Computers, Vol. 42, No. 3, Mar. 1993, pp. 340352.
[4] G. Edirisooriya and J. Robinson, "Aliasing in MultipleValued Test Data Compaction," Proc. 22nd Int'l Symp. MultipleValued Logic, pp. 4350, 1992.
[5] D.M. Miller, J.C. Muzio, M. Serra, X. Sun, S. Zhang, and R.D. McLeod, "Cellular Automata Techniques for Compaction Based BIST," Proc. IEEE Int'l Symp. Circuits and Systems, pp. 1,8931,896, 1991.
[6] M. Serra et al., "The Analysis of OneDimensional Linear Cellular Automata and Their Aliasing Properties," IEEE Trans. ComputerAided Design, vol. 9, no. 7, pp. 767778, July 1990.
[7] Ph. Tsalides, T.A. York, and A. Thanailakis, "Pseudorandom Number Generators for Systems Based on Linear Cellular Automata," IEE Proc. Part E: Computers and Digital Techniques, vol. 138, pp. 241249, 1991.
[8] S. Zhang, R. Byrne, J.C. Muzio, and D.M. Miller, "Why Cellular Automata Are Better than LFSRs as BuiltIn SelfTest Generators for SequentialType Faults," Proc. IEEE Int'l Symp. Circuits and Systems, vol. 1, pp. 6972, 1994.
[9] P. Guan and Y. He, "Exact Rules for Deterministic Cellular Automata with Additive Rules," J. Statistical Physics, vol. 43, pp. 463478, 1986.
[10] E. Jen, "Global Properties of Cellular Automata," J. Statistical Physics, vol. 43, pp. 219242, 1986.
[11] H.Y. Lee and Y. Kawahara, "On Dynamical Behaviours of Cellular Automata ca60," Bulletin Informatics and Cybernetics, vol. 25, pp. 2125, 1992.
[12] M. Nohmi, "On a Polynomial Representation of Finite Linear Cellular Automata," Bulletin Informatics and Cybernetics, vol. 24, pp. 137145, 1991.
[13] S. Wolfram, "Statistical Mechanics of Cellular Automata," Review Modern Physics, vol. 55, pp. 601644, 1983.
[14] S. Wolfram, "Universality and Complexity in Cellular Automata," Physica, vol. 10D, pp. 135, 1984.
[15] Z. Zilic and Z. Vranesic,“Current mode CMOS Galois field circuits,” Proc. 23rd Int’l Symp. MultipleValued Logic, pp. 245250, May 1993.
[16] K. Cattell and J.C. Muzio, "Synthesis of OneDimensional Linear Hybrid Cellular Automata," IEEE Trans. ComputerAided Design, vol. 15, pp. 325335, 1996.
[17] J.M. Mesirov and M.M. Sweet, "Continued Fraction Expansions of Rational Expressions with Irreducible Denominators in Characteristic 2," J. Number Theory, vol. 27, pp. 144148, 1987.
[18] R. Lidl and H. Niederreiter,An Introduction to Finite Fields and Their Applications.Cambridge: Cambridge Univ. Press, 1986.
[19] R.J. McEliece, Finite Fields for Computer Scientists and Engineers. Kluwer Academic, 1987.
[20] T. Hansen and G.K. Mullen, "Primitive Polynomials Over Finite Fields," Math. Comp., vol. 59, pp. 639643, 1992.
[21] K. Cattell and M. Serra, "The Analysis of One Dimensional MultipleValued Linear Cellular Automata," Proc. 20th Int'l Symp. MultipleValued Logic, pp. 402409, 1990.
[22] H.S. Stone, Discrete Mathematical Structures and Their Applications. Science Research Associates Inc., 1973.