This paper studies practical algorithms for dealing with a particular family of cellular automata, which has recently been proved computationally equivalent to linear conjunctive grammars. The relation between these grammars and these automata resembles that between regular expressions and finite automata: while the former are better suited for human use, the latter are considerably easier to implement. In this paper, an algorithm for converting an arbitrary linear conjunctive gram-mar to an equivalent automaton is proposed, and different techniques of reducing the size of existing automata are studied.