Universality and decidability of number-conserving cellular automata

Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the definition of the property to include cellular automata with any set of states in Z, and show that they can be always extended to "usual" NCCA with contiguous states. We show a way to simulate any one dimensional CA through a one-dimensional NCCA, proving the existence of intrinsically universal NCCA. Finally, we give an algorithm to decide, given a CA, if its states can be labeled with integers to produce a NCCA, and to find this relabeling if the answer is positive. (C) 2002 Elsevier Science B.V. All rights reserved.