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Abstract: We show that a wide variety of non-linear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depth O(log 2 t) using gates with binary inputs, or O(log t) depth if "sum mod p" gates with an unbounded number of inputs are allowed. Thus these CAs can be predicted by (idealized) parallel computers much faster than by explicit simulation, even though they are non-linear. This class includes any CA whose rule, when ... (Update)
Context of citations to this paper: More
...behaviour in the original semigroup. We require a product whose components can be guaranteed to compose to give global behaviours. Moore (1998) provides such a notion of product and decomposition; however, we need a more generally applicable notion of composition than the...
...and Circuit Value can have varying complexities. Previous results for the associative case (groups and semigroups) include the following [3, 7, 22]: Expression Evaluation Circuit Value non solvable NC 1 complete P complete solvable ACC 0 ACC 1 DET In this paper, we will...
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BibTeX entry: (Update)
C. Moore, "Predicting non-linear cellular automata quickly by decomposing them into linear ones." To appear in Physica D, Proceedings of the International Workshop on Lattice Dynamics.. http://citeseer.ist.psu.edu/article/moore97predicting.html More
@article{ moore98predicting,
author = "C. Moore",
title = "Predicting non-linear cellular automata quickly by decomposing them into linear ones",
journal = "Physica (D)",
volume = "111",
pages = "27--41",
year = "1998",
url = "citeseer.ist.psu.edu/article/moore97predicting.html" }
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97 Limits to Parallel Computation: P-Completeness Theory - Greenlaw, Hoover et al. - 1995
82 The Theory of Groups (context) - Hall - 1976
70 Statistical Mechanics of Cellular Automata (context) - Wolfram - 1983
51 Lower bounds for the size of circuits of bounded depth with .. (context) - Razborov - 1987
45 Parity, circuits, and the polynomialtime hierarchy (context) - Furst, Saxe et al. - 1984
43 Bounded-width polynomial-size branching programs recognize e.. (context) - Barrington - 1989
37 Universal computation in simple onedimensional cellular auto.. (context) - Lindgren, Nordahl - 1990
29 Theory of Groups of Finite Order (context) - Burnside - 1911
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19 Quasigroups and Loops: Theory and Applications (context) - Chein, Pflugfelder et al. - 1990
17 Algebraic properties of cellular automata - Martin, Odlyzko et al. - 1984
16 Quasi-linear cellular automata - Moore - 1997
12 Finite Groupoids and their Applications to Computational Com.. - Lemieux - 1996
11 Sigma 1 1 formulae on finite structures (context) - Ajtai - 1983
11 Cryptography with Cellular Automata (context) - Wolfram - 1986
9 Non-Abelian cellular automata - Moore
9 Cellular automata as algebraic systems (context) - Pedersen - 1992
8 The computational complexity of generating random fractals - Machta, Greenlaw - 1996
8 Computational mechanics of cellular automata: an example - Hanson, Crutchfield
7 Attractor vicinity decay for a cellular automaton (context) - Crutchfield, Hanson - 1993
6 Circuits with monoidal gates (context) - Beaudry, McKenzie et al. - 1993
4 Fast computation of additive cellular automata (context) - Robinson - 1987
4 Predicting lattice gases is P-complete - Moore, Nordahl
4 Algebraic properties of the block transformation on cellular.. - Moore, Drisko
3 Exact solvability and quasiperiodicity of one-dimensional ce.. (context) - Jen - 1990
3 Partially permutive cellular automata: analysis via tilings .. (context) - Eloranta - 1992
3 Majority-vote cellular automata, Ising dynamics, and Pcomple.. - Moore
3 Circuits and expressions with non-associative gates - Berman, Drisko et al.
2 personal communication (context) - Rusin
1 Nasser and M (context) - Boccara - 1991
1 On pseudovarieties (context) - Eilenberg, Schutzenberger - 1976
1 Additive cellular automata with external inputs (context) - Arrowsmith, Dow - 1995
1 Computation theoretical aspects of cellular automata (context) - Hurd, Yu - 1990
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