Number-conserving cellular automata I: decidability

Number-conserving cellular automata I: decidability

We prove that de6nitions of number-conserving cellular automata found in literature are equivalent. A necessary and su9cient condition for cellular automata to be number-conserving is proved. Using this condition, we give a quasi-linear time algorithm to decide number-conservation. c © 2002 Elsevier Science B.V. All rights reserved.

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 state...

Number conserving cellular automata: new results on decidability and dynamics

In the last ten years number conserving cellular automata (NCA) have received greater and greater attention. This interest is confirmed by the hundreds of papers in international conferences or journals since their introduction in [15]. They essentially model particle systems ruled by conservation laws of mass or energy with applications in a wide range of scientific disciplines. For example, t...

Eventually Number-Conserving Cellular Automata

We present a preliminary study of a new class of two-input cellular automaton rules called eventually number-conserving rules characterized by the property of evolving after a finite number of time steps to states whose number of active sites remains constant. Viewed as models of systems of interacting particles, these rules obey a kind of Darwinian principle by either annihilating unnecessary ...

State-Conserving Cellular Automata