A New Class of Automata Networks

A new class of automata networks is defined. Their evolution rules are determined by a probability measure p on the set of all integers Z and an indicator function I_A on the interval [0,1]. It is shown that any cellular automaton rule can be represented by a (nonunique) rule formulated in terms of a pair (p,I_A). This new class of automata networks contains discrete systems which are not cellular automata. Some of their properties are discussed.Comment: Uses elsart.cls document class. Five figures (two in EPS format

Randomized Cellular Automata

We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined on random directed graphs with constant out-degrees and evolve according to cellular automaton rules. For some families of rules, a few typical a priori unexpected results are presented.Comment: 13 pages, 7 figure

Critical behavior of a cellular automaton highway traffic model

We derive the critical behavior of a CA traffic flow model using an order parameter breaking the symmetry of the jam-free phase. Random braking appears to be the symmetry-breaking field conjugate to the order parameter. For $v_{\max}=2$, we determine the values of the critical exponents $\beta$, $\gamma$ and $\delta$ using an order-3 cluster approximation and computer simulations. These critical exponents satisfy a scaling relation, which can be derived assuming that the order parameter is a generalized homogeneous function of $|\rho-\rho_c|$ and p in the vicinity of the phase transition point.Comment: 6 pages, 12 figure

On the existence of a variational principle for deterministic cellular automaton models of highway traffic flow

It is shown that a variety of deterministic cellular automaton models of highway traffic flow obey a variational principle which states that, for a given car density, the average car flow is a non-decreasing function of time. This result is established for systems whose configurations exhibits local jams of a given structure. If local jams have a different structure, it is shown that either the variational principle may still apply to systems evolving according to some particular rules, or it could apply under a weaker form to systems whose asymptotic average car flow is a well-defined function of car density. To establish these results it has been necessary to characterize among all number-conserving cellular automaton rules which ones may reasonably be considered as acceptable traffic rules. Various notions such as free-moving phase, perfect and defective tiles, and local jam play an important role in the discussion. Many illustrative examples are given.Comment: 19 pages, 4 figure