Accepted:
15 Oct 1998
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/vol06/park/ | © Copyright 1998 | |||
| Volume 06 | Received: Accepted: |
01 Jul 1998 15 Oct 1998 |
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A Categorical Representation of the State Transition Graph of Finite Cellular Automata
Jung-Hee, Park, Hyen-Yeal, Lee |
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| Abstract | |
| One-dimensional cellular automata ÊA(m), B(m), C(m) and D(m) with two states (0 and 1) and four different boundary conditions such as 0-0, 0-1, 1-0 and 1-1 respectively are studied on the self-reproduction of the state transition graph by the categorical representation. The simple recursive formulae of the fifteen rules such as rules 0, 3, 12, 15, 48, 51, 60, 192, 195, 204, 207, 240, 243, 252 and 255 among 256 rules were found, which are used to self-reproduce the state transition graph. It is also found that these fifteen rules satisfy that A(m), B(m), C(m) and D(m) are all equal or A(m) is equal to B(m) and C(m) is equal to D(m). Moreover, such finite cellular automata are classified according to the recursive formulae found. | |
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