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A necessary and suucient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two diierent forms of simpler and more visual representations of these rules are given, and their ow diagrams are determined. Various examples are presented and applications to car traac are indicated. Two nontrivial(More)
  • H Fukś
  • 1999
We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to a well-known lattice path counting problem. Assuming infinite lattice size and random initial configuration, the flow(More)
  • Henryk Fukś
  • 2002
We present a probabilistic cellular automaton (CA) with two absorbing states which performs classification of binary strings in a nondeterministic sense. In a system evolving under this CA rule, empty sites become occupied with a probability proportional to the number of occupied sites in the neighborhood, while occupied sites become empty with a(More)
We investigate individual packet delay in a model of data networks with table-free, partial table and full table routing. We present analytical estimation for the average packet delay in a network with small partial routing table. Dependence of the delay on the size of the network and on the size of the partial routing table is examined numerically.(More)
We investigate second order additive invariants in elementary cellular automata rules. Fundamental diagrams of rules which possess additive invariants are either linear or exhibit singularities similar to singularities of rules with first-order invariant. Only rules which have exactly one invariants exhibit singularities. At the singularity, the current(More)