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This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with respect to Turing and circuit universality, we discuss construction methods for small intrinsically universal cellular automata before discussing techniques for proving non universality.
Signals are a classical tool used in cellular automata constructions that proved to be useful for language recognition or firing-squad synchronisation. Particles and collisions formalize this idea one step further, describing regular nets of collidin
We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial configuration of th
In this paper, we study reversibility of one-dimensional(1D) linear cellular automata(LCA) under null boundary condition, whose core problems have been divided into two main parts: calculating the period of reversibility and verifying the reversibili
Cellular Automata have been used since their introduction as a discrete tool of modelization. In many of the physical processes one may modelize thus (such as bootstrap percolation, forest fire or epidemic propagation models, life without death, etc)
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter, and features a global symmetry. One then extends th