Cristopher Moore Santa Fe Institute September 25, 1995  Home/Search
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Abstract: Simulating a cellular automaton (CA) for t time-steps into the future requires t serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed linear because they obey a principle of superposition. This allows them to be predicted efficiently, in serial time O(t) [1] or O(log t) in parallel. (Update)
Context of citations to this paper: More
...quickly, in O(log t) or O(log 2 t) time. Thus in special cases the CA prediction problem can be in NC, even for some nonlinear rules [5, 6]. On the other hand, some systems such as lattice gases [7] sandpiles [8] and zero temperature Ising dynamics [9] are P complete to...
.... will also help us tell when there are fast algorithms for predicting cellular automata whose rules correspond to certain algebras, as in [17, 18]. 2 Algebraic preliminaries We will use the following terms. For the theory of quasigroups and loops, we recommend [20] as an...
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BibTeX entry: (Update)
C. Moore, "Quasi-linear cellular automata." Physica D 103 (1997) 100-132, Proceedings of the International Workshop on Lattice Dynamics. http://citeseer.ist.psu.edu/moore97quasilinear.html More
@article{ moore97quasilinear,
author = "C. Moore",
title = "Quasi-linear cellular automata",
journal = "Physica (D)",
volume = "103",
pages = "100--132",
year = "1997",
url = "citeseer.ist.psu.edu/moore97quasilinear.html" }
Citations (may not include all citations):1911 Introduction to Automata Theory (context) - Hopcroft, Ullman - 1979
951 Computational Complexity (context) - Papadimitriou - 1994
136 Efficient Parallel Algorithms (context) - Gibbons, Rytter - 1988
78 Seminumerical Algorithms (context) - Knuth - 1981
70 Statistical Mechanics of Cellular Automata (context) - Wolfram - 1983
52 Latin Squares and their Applications (context) - D'enes, Keedwell - 1974
37 Universal Computation in Simple OneDimensional Cellular Auto.. (context) - Lindgren, Nordahl - 1990
30 Turbulent Pattern Bases for Cellular Automata - Crutchfield, Hanson - 1993
17 Algebraic Properties of Cellular Automata - Martin, Odlyzko et al. - 1984
11 Cryptography with Cellular Automata (context) - Wolfram - 1986
9 Cellular Automata as Algebraic Systems (context) - Pedersen - 1992
5 Cryptography with Dynamical Systems - Gutowitz - 1993
4 Co-ordinatizing Steiner Systems (context) - Ganter, Werner - 1980
4 Fast Computation of Additive Cellular Automata (context) - Robinson - 1987
3 Partially Permutive Cellular Automata; Analysis via Tilings .. (context) - Eloranta - 1992
3 Monomial Cellular Automata (context) - Bartlett, Garzon - 1993
2 Demosian systems of quasigroups (context) - Sade - 1961
2 Cyclic Cellular Automata and Related Processes (context) - Fisch - 1990
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Non-Abelian Cellular Automata - Moore (1995) (Correct)
Algebraic Properties of the Block Transformation on Cellular.. - Moore, Drisko (1995) (Correct)
Recursion Theory on the Reals and Continuous-time Computation - Moore (1995) (Correct)
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