Paper Info
Title
Real-Time Generation of Primes by a One-Dimensional Cellular Automaton with 11 States
Abstract
A 11-state one-dimensional cellular automaton is constructed which generates the primes in the following sense: The content of the 0-th cell at time t is equal to 1 if t is a prime, and is equal to 0 otherwise. The neighbourhood type of this CA is (-1, 0, 1), i.e. the most usual one. At time t = 0 only the 0-th cell is in the non-quiescent state (here 0 is not the quiescent state). Further, a one-dimensional CA is constructed with the radius 12 but with two states only which also generates the primes. (At time t - 0 only the 1-st cell is in non-quiescent state.) Also a generalized Pascal triangle with 83 distinct elements is constructed which generates the odd primes in a similar sense. Hence the primes can be real-time generated also by a 83-state one-dimensional CA with the neighborhood type (-1,1).
Year
DOI
Venue
1997
10.1007/BFb0029979
MFCS
Keywords
Field
DocType
real-time generation,one-dimensional cellular automaton,cellular automaton,real time
Prime (order theory),Cellular automaton,Discrete mathematics,Pascal's triangle,Elementary cellular automaton,Automata theory,Combinatorics,Continuous automaton,Mobile automaton,Mathematics
Conference
ISBN
Citations 
PageRank 
3-540-63437-1
5
0.52
References 
Authors
2
1
Name
Order
Citations
PageRank
Ivan Korec19821.18