Steven J. Janke

The probability of splitters in a list

Abstract A list a (1),…, a ( n ) splits if there exists j with a ( i ) ≤ a ( j ) if i j and a ( i ) ≥ a ( j ) if i > j . We show, for lists of distinct elements, that the probability of a list splitting is asymptotic to 2 n ( n being the length of the list).

Practical Fault Tolerant 2D Cellular Automata

Cellular automata often suffer from a level of brittleness that makes them susceptible to even the smallest unexpected environmental changes. We propose a method of converting CAs into more robust structures called meta-CAs that utilize cell redundancy along with added rules to correct errors and reproduce the functionality of the original CA. We show that the use of these meta-CAs can greatly increase the probability of CAs being intact when executing in an environment where cells fail on each step with a small probability.