On the relationship between fuzzy and Boolean cellular automata

Fuzzy cellular automata (FCA) are continuous cellular automata where the local rule is defined as the “fuzzification" of the local rule of a corresponding Boolean cellular automaton in disjunctive normal form. In this paper, we are interested in the relationship between Boolean and fuzzy models and, for the first time, we analytically show the existence of a strong connection between them by focusing on two properties: density conservation and additivity. We begin by showing that the density conservation property, extensively studied in the Boolean domain, is preserved in the fuzzy domain: a Boolean CA is density conserving if and only if the corresponding FCA is sum preserving. A similar result is established for another novel “spatial" density conservation property. Second, we prove an interesting parallel between additivity of Boolean CA and oscillations of the corresponding fuzzy CA around its fixed point. In fact, we show that a Boolean CA is additive if and onl...

• Type: Journal
• Year: 2011
• Where: TCS
• Authors: Heather Betel, Paola Flocchini
• Keywords: Boolean CA, Cellular Automata, Density Conservation, TCS 2011, Theoretical Computer Science