Group Properties of Cellular Automata and VLSI Applications

IEEE Transactions on Computers

Volumn C-35, Issue 12, 1986, Pages 1013-1024

  Pries, Werner ^a   Thanailakis, Adonios ^b   Card, Howard C ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

^b DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

Author keywords

Automata theory; cellular automata; computation; group theory; mesh connected computers; modular arithmetic; VLSI

Indexed keywords

INTEGRATED CIRCUITS, VLSI - APPLICATIONS; MATHEMATICAL TECHNIQUES - GRAPH THEORY;

CELLULAR AUTOMATA; COMPUTATIONAL STRUCTURES; GROUP GLOBAL STATES PERMUTATIONS; MODULO ARITHMETIC UNITS; RULE MULTIPLICATION;

AUTOMATA THEORY;

EID: 0022895656     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/TC.1986.1676709     Document Type: Article

References (12)

1. S. Wolfram, “Statistical mechanics of cellular automata,” Rev. Mod. Physics, vol. 55, no. 3, 601–644, 1983.
2. B. Hayes, “Computer recreations,” Scientific Amer., pp. 12–21, Mar. 1984.
3. C. L. Seitz, “Concurrent VLSI architectures,” IEEE Trans. Comput., vol. C-33, pp. 1247–1265, Dec. 1984.
4. J. H. Conway, Winning Ways for your Mathematical Plays, Vol. 2, E. R. Berlekamp, J. H. Conway, and R. K. Guy Eds. London: Academic, 1982, ch. 25.
5. C. D. Thompson anc H. T. Kung, “Sorting on a mesh-connected parallel computer,” Commun. Ass. Comput. Mach., vol. 20, pp. 263–271, 1977.
6. D. A. Lind, “Application of ergodic theory and sofic systems to cellular automata,” in Cellular Automata, Physica 10D, D. Farmer, T. Toffoli, and S. Wolfram Eds. Amsterdam, The Netherlands: North Holland, 1984, 36–44.
7. O. Martin, A. M. Odlyzko, and S. Wolfram, “Algebraic properties of cellular automata,” Commun. Math. Phys., vol. 93, p. 219, 1984.
8. D. B. Chesnut, Finite Groups and Quantum Theory. Melbourne, FL: Krieger, 1982.
9. B. Baumslag and B. Chandler, Schaum's Outline on Group Theory. New York: McGraw-Hill, 1968.
10. A. Thanailakis, W. Pries, C. J. Zarowski, and H. C. Card, “Algebraic structure of VLSI finite-state machines based on linear cellular automata,” to be published.
11. C. D. Thompson, “Area-time complexity for VLSI,” in Proc. 11th Ann. ACM Symp. Theory of Comput., 1979, pp. 81–88.
12. S. S. Yau and J. Chung, “On the design of modulo arithmetic units based on cyclic groups,” IEEE Trans. Comput., vol. C-25, pp. 1057–1067, Nov. 1976.