On Routine Evolution of Complex Cellular Automata

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Presentation transcript:

On Routine Evolution of Complex Cellular Automata Michal Bidlo bidlom@fit.vutbr.cz Humies 2016

Presentation outline This entry is based on the paper: M. Bidlo: On Routine Evolution of Complex Cellular Automata. In: IEEE Transactions on Evolutionary Computation, PP(99), 2016 (in print) Research overview & challenges Reasons for human competitiveness Why should this paper win

Topic overview Uniform cellular automata (CA) represent a class of complex systems in which the behavior emerges from local interactions between cells. The design of transition functions for CA becomes very difficult with the increasing number of cell states, i.e. the aim is to automate this process. An efficient encoding of transition functions is needed in order to solve a given application (which was a subject of the proposed paper). Some existing CA benchmarks: Input: X=4 Output: Y=X2 Langton's self-replicating loop Codd's construction arm Wolfram's generic squaring CA

Why is the CA design hard? The design of transition rules for CA is not intuitive. A need to explore huge spaces of potential solutions, e.g. for 1D CA, 8 states, 3-cell neighborhood there are over 2.4x10462 transition functions, the 2D CA, 6 states, 5-cell neighborhood induces more than 8.0x106050 transition functions. Sometimes it is even not known whether a solution exists, so the evolution is a real discovery. In our case: given some input and expected output, the EA should find both the CA behavior leading to the output and the transition rules determining how to achieve it.

Common approach CA have been designed and studied analytically, for example: Langton's loop Byl's loop The loop of Chou-Reggia Conway's Game of Life self-replicating loops Wolfram's prime universal computing number generator These were usually designed by means of well-established engineering methods. Can evolution bring us something more? YES, IT CAN!

The proposed evolutionary approach Instead of using extensive chromosomes: we introduced a special encoding using conditions: This allowed us to discover processes in CA, which have never been observed before. For example: a replicating loop grown from a seed 5 0 5 1 2 3 0 5 4 4 5 0 2 2 2 0 2 3 0 4 4 0 3 2 1 1 3 4 1 1 4 4 2 4 3 0 3 1 0 0 5 0 0 3 0 1 2 1 0 0 3 2 0 4 0 2 0 3 4 5 0 0 4 0 5 1 0 0 0 0 2 3 3 0 0 3 4 3 1 4 0 1 2 1 0 0 2 0 1 0 1 5 5 3 2 1 1 0 2 1 1 0 5 1 1 1 5 0 1 4 0 1 5 1 3 3 1 2 4 0 1 3 0 3 2 5 3 5 1 1 0 0 4 0 2 0 5 5 4 2 2 2 1 5 0 0 3 1 4 5 5 1 3 3 3 4 4 1 0 4 3 3 1 0 5 3 1 3 1 0 2 4 5 1 5 5 5 5 1 3 2 0 5 5 3 3 0 1 4 2 1 3 5 0 2 3 2 1 2 2 0 2 4 4 0 5 3 2 3 1 2 3 2 1 1 0 3 4 0 1 1 0 1 5 5 0 5 5 2 2 0 1 1 1 3 4 2 1 1 2 1 3 0 2 5 3 3 5 3 3 5 4 2 2 1 0 4 0 0 3 2 3 1 1 5 3 2 2 2 2 2 3 4 0 5 3 1 0 0 1 5 3 4 1 5 3 4 1 1 5 4 3 1 0 0 1 1 3 0 0 2 5 1 1 2 1 4 3 0 1 4 4 1 3 3 4 2 3 3 0 0 1 0 3 1 5 0 4 4 1 1 1 3 1 0 2 4 0 3 2 5 0 4 0 2 3 5 1 0 2 5 0 5 0 0 1 4 2 0 2 3 4 4 0 1 2 2 3 5 0 0 4 2 1 0 0 4 4 2 4 4 2 5 5 3 3 2 2 2 2 2 1 1 2 2 3 4 0 3 1 1 0 0 0 3 2 4 0 2 5 0 1 4 3 2 1 1 3 1 4 2 4 5 2 0 0 5 2 3 5 2 1 3 1 3 2 2 1 4 2 5 1 3 5 5 3 3 2 2 2 4 5 1 5 0 2 4 2 1 2 5 0 1 3 5 4 4 5 5 2 4 2 5 1 4 3 1 4 0 0 3 4 3 5 0 1 1 0 4 0 0 2 3 5 3 2 0 4 5 0 1 0 2 2 4 5 1 3 3 3 3 4 4 2 1 4 5 1 2 3 2 0 4 5 4 4 2 3 0 1 0 4 1 1 2 0 2 1 4 1 1 1 5 3 5 3 3 4 2 4 0 1 1 0 2 4 3 2 5 5 4 5 0 3 3 5 0 2 1 2 3 0 0 3 3 2 2 3 2 2 0 2 1 2 0 2 0 1 2 3 1 2 5 3 4 4 0 5 3 1 2 4 2 0 1 0 2 5 3 0 0 2 3 1 2 1 2 4 5 0 0 3 1 2 5 5 2 1 3 0 4 5 3 0 3 4 3 2 3 4 4 4 5 0 2 3 1 5 0 5 5 3 3 3 3 1 1 3 1 4 4 3 4 4 0 0 0 0 0 4 2 1 1 1 2 3 4 1 5 4 1 1 5 2 5 0 3 3 5 3 2 2 4 3 0 5 4 3 4 5 1 0 3 3 2 3 2 4 3 4 0 4 2 1 2 5 5 5 0 4 0 4 4 0 1 4 0 1 5 2 0 3 0 3 5 4 2 3 1 5 3 2 4 2 2 1 2 5 2 1 0 5 3 4 5 0 2 3 5 2 1 5 5 0 3 1 3 5 5 2 0 5 1 0 3 1 5 0 4 2 1 5 3 4 2 4 1 5 1 1 4 2 1 0 2 1 1 0 1 4 2 1 4 3 1 2 3 0 1 1 3 4 5 3 2 0 0 1 1 2 1 0 3 2 2 4 4 0 1 2 4 2 2 2 0 0 2 0 1 0 4 5 5 1 1 1 2 2 1 5 1 4 1 0 1 3 5 0 3 4 4 1 3 3 0 4 0 2 5 5 5 4 0 1 2 1 5 4 0 1 3 4 3 1 1 5 2 1 1 0 4 2 4 5 0 2 0 4 3 1 4 3 4 2 1 0 2 0 3 3 2 3 4 1 5 2 3 5 3 0 5 4 4 0 5 0 1 2 3 4 5 5 3 3 2 1 2 2 2 5 5 1 4 1 1 5 5 0 5 0 5 2 2 2 3 4 2 4 3 2 2 5 5 1 4 5 2 2 4 0 4 3 5 3 3 4 0 2 2 0 2 3 2 2 2 0 1 0 4 4 0 3 0 4 2 1 1 3 1 5 3 5 2 3 5 0 2 3 0 3 4 1 4 4 4 4 4 0 5 5 1 5 3 2 5 1 4 3 4 0 4 3 0 0 4 4 3 5 5 5 5 4 2 0 1 0 4 3 5 5 4 2 0 4 3 1 0 3 2 0 4 5 2 2 5 3 5 0 5 5 2 1 5 1 1 1 0 1 3 3 1 5 0 5 0 1 1 2 0 5 0 4 2 2 4 1 3 3 2 5 0 5 0 1 5 0 1 0 4 4 3 1 3 5 4 3 5 3 5 1 4 4 4 4 4 0 5 0 0 1 5 1 4 1 1 1 4 1 3 2 3 2 3 4 0 2 5 5 2 0 5 1 4 5 4 5 5 5 1 3 2 1 3 3 5 0 0 3 5 4 1 1 2 5 4 3 5 4 0 2 2 5 3 2 4 5 5 2 5 1 1 0 5 5 3 1 2 2 2 3 4 0 1 5 0 5 5 4 1 4 1 3 2 3 5 4 5 0 0 4 1 0 5 1 2 3 5 0 2 1 2 2 1 1 5 1 3 0 5 3 3 3 5 0 5 4 2 5 2 5 5 1 2 0 4 2 1 1 4 3 4 2 5 4 0 0 2 3 5 1 2 1 4 0 3 2 5 5 4 1 0 3 3 1 1 5 1 3 4 2 1 4 1 3 3 5 1 0 5 0 4 4 5 2 4 3 0 3 1 1 2 3 5 1 5 1 5 1 4 1 3 2 2 4 1 3 3 1 4 0 4 0 0 1 1 5 4 5 5 2 1 3 1 4 0 2 4 2 2 0 1 1 2 1 5 5 3 2 3 2 3 3 3 0 3 0 2 5 2 3 4 3 1 2 2 1 0 0 2 5 2 1 0 5 0 4 2 1 4 3 3 0 2 5 5 2 1 5 1 4 3 0 2 3 1 4 0 3 5 0 0 1 5 2 1 0 2 3 0 4 5 4 3 4 4 0 5 0 3 4 3 4 0 1 1 2 3 2 0 0 2 2 0 3 4 5 5 3 4 5 1 1 5 3 4 2 4 0 1 1 1 3 2 0 1 1 2 0 5 3 4 4 1 1 5 0 3 5 3 1 4 3 5 1 1 5 4 1 4 0 2 3 0 5 4 1 3 2 0 4 2 0 3 3 5 1 3 2 3 1 2 4 0 1 0 2 3 4 4 2 3 4 5 5 4 2 2 2 1 4 1 3 2 4 3 4 3 4 2 5 1 5 4 1 5 4 2 1 2 2 2 2 1 3 5 1 2 1 4 5 0 3 5 3 1 1 0 0 3 3 5 5 1 5 5 3 0 3 1 2 1 0 4 2 0 1 1 3 0 2 1 1 1 0 2 1 2 1 3 5 4 3 0 5 5 2 3 4 2 0 0 2 2 3 5 1 0 0 2 1 5 4 2 2 2 1 0 2 4 2 0 4 0 1 0 4 3 4 1 5 5 3 2 3 0 5 3 3 3 5 0 0 3 5 4 2 4 3 0 1 1 4 3 2 2 0 4 0 3 2 3 3 0 0 5 5 3 5 4 3 2 1 3 3 2 3 4 0 5 0 4 2 1 2 1 0 0 4 1 0 2 5 1 0 2 3 4 2 1 5 4 1 4 4 4 5 3 2 1 5 5 4 3 2 0 4 2 5 2 2 1 4 5 0 1 4 1 2 4 1 2 0 0 0 5 0 0 0 5 1 3 2 4 2 5 3 4 0 0 4 0 4 4 5 2 3 2 0 3 4 0 3 3 0 4 0 3 4 0 1 3 3 1 0 4 2 5 0 0 2 5 4 2 2 0 3 2 2 2 4 2 3 1 3 0 3 0 0 5 2 2 4 5 1 0 2 4 1 3 2 5 2 1 5 4 5 2 2 4 0 4 5 2 3 0 3 5 5 1 0 2 0 5 4 2 0 5 0 1 5 4 0 4 3 0 5 5 5 0 3 0 4 1 4 3 2 0 4 5 1 3 3 4 1 0 2 5 3 2 1 5 4 1 0 5 0 5 5 0 3 0 3 5 2 0 0 5 2 1 5 4 3 0 4 4 5 0 3 1 0 3 0 3 0 3 4 2 5 0 2 0 0 0 5 3 0 2 0 5 5 1 2 4 3 3 0 2 3 5 1 2 0 2 3 0 0 3 3 0 4 2 2 5 4 2 3 4 5 5 4 4 2 3 2 1 4 0 4 3 2 1 4 5 3 0 5 4 0 4 0 0 3 0 2 0 4 4 5 4 5 0 2 3 2 2 0 1 0 1 3 3 2 2 3 1 2 2 4 2 1 0 2 4 4 3 5 1 2 3 2 4 3 3 4 5 2 3 0 0 1 1 2 3 1 5 5 4 2 4 4 3 3 4 4 5 4 1 3 1 5 3 0 4 1 1 1 1 4 1 4 1 4 0 5 5 2 5 0 4 3 4 3 1 5 2 2 5 3 5 4 2 4 4 0 1 1 2 1 1 5 3 1 5 3 3 5 3 1 5 5 0 3 5 1 2 1 5 2 4 0 3 0 1 3 3 3 1 1 0 0 5 5 3 1 4 3 3 4 0 0 3 1 4 3 3 0 4 5 5 5 2 2 2 2 0 2 1 3 4 3 1 1 5 5 2 3 0 3 4 5 0 0 1 0 4 3 3 2 1 3 3 5 5 0 0 3 5 5 2 3 0 0 2 2 3 3 2 5 2 4 5 4 0 1 2 5 2 1 5 5 1 3 3 0 3 5 0 5 3 1 2 0 4 0 4 2 2 4 0 5 0 2 4 1 4 1 1 2 2 1 5 0 4 2 2 3 1 2 5 5 4 2 5 4 2 3 3 1 2 0 5 4 0 4 4 3 4 3 0 4 0 1 0 3 5 4 2 2 3 1 2 2 0 2 5 3 3 2 4 5 0 5 2 2 3 5 2 0 5 5 2 3 3 1 3 5 5 3 4 2 3 4 4 2 1 0 2 0 4 2 0 2 2 1 4 2 4 4 3 0 1 1 0 0 0 4 4 3 3 5 5 3 2 2 3 4 4 4 3 5 1 3 2 1 1 4 5 3 1 3 2 2 5 4 4 2 2 1 4 4 5 1 2 1 2 1 5 5 5 2 4 3 2 3 1 2 0 5 3 1 4 5 3 0 4 1 3 2 0 0 5 1 5 1 4 2 1 5 5 0 2 2 2 2 3 3 0 5 2 2 3 0 1 3 0 1 5 0 2 0 2 3 3 2 2 2 5 3 4 1 4 1 1 0 5 4 5 1 5 4 4 3 5 4 3 4 2 4 2 5 4 4 0 2 5 3 0 5 0 1 4 5 3 4 2 5 3 2 4 1 3 0 3 4 0 3 0 0 5 1 1 3 0 4 4 0 3 2 1 4 5 0 1 1 1 4 0 2 0 3 3 3 4 5 1 3 3 5 4 1 4 1 0 3 3 4 4 4 3 2 0 0 2 4 5 4 0 0 0 2 2 4 1 3 1 5 4 1 5 4 0 2 1 2 0 0 3 5 5 3 5 4 5 3 3 0 0 5 3 2 2 3 3 5 1 3 2 3 2 3 1 1 0 1 4 2 2 4 4 0 3 4 4 1 4 3 3 3 4 2 2 3 1 0 2 5 3 1 4 1 1 5 5 3 3 3 0 2 2 5 3 1 1 5 0 1 2 5 4 1 4 4 1 3 2 3 2 3 3 1 2 0 5 3 3 3 3 5 0 1 2 1 2 4 2 2 4 1 1 0 5 2 5 1 3 2 2 5 0 5 1 2 1 2 4 2 3 0 5 2 5 1 3 5 5 0 4 2 3 2 0 0 0 4 0 4 4 3 1 0 1 2 4 4 4 2 5 2 4 4 2 2 1 3 1 5 5 1 0 0 1 5 5 0 2 3 5 0 0 0 0 2 5 0 5 3 5 1 0 2 2 2 4 2 5 2 0 0 1 2 1 1 4 4 2 2 1 3 1 2 2 1 4 4 1 5 0 0 1 2 4 4 1 4 0 4 2 5 1 4 2 1 2 3 4 1 1 0 4 0 5 5 1 3 2 5 4 1 5 5 5 2 3 3 0 1 1 3 1 0 5 4 2 5 3 3 0 0 4 4 1 5 5 5 3 1 3 4 0 1 3 5 0 0 4 4 2 2 1 0 3 4 0 1 1 5 1 1 5 0 2 3 0 3 4 0 1 3 3 0 4 2 4 1 1 2 2 4 1 4 0 1 0 0 1 0 4 2 2 4 5 0 1 5 0 2 5 2 3 0 5 2 5 2 2 4 4 5 5 5 5 4 2 4 1 0 2 4 2 3 2 5 1 1 5 3 4 4 2 3 3 0 4 0 5 2 1 5 3 1 0 1 2 2 3 4 4 5 2 1 5 0 2 1 2 4 0 5 2 1 4 2 4 0 5 0 3 2 5 5 0 4 3 0 2 0 0 0 3 5 0 4 0 5 0 1 2 0 5 4 3 2 5 4 1 3 1 0 2 4 2 5 4 4 4 0 2 4 5 5 5 2 3 2 0 5 3 0 4 3 2 1 5 1 2 0 5 1 4 2 1 4 3 1 2 0 3 4 0 5 4 0 5 3 2 1 2 0 5 0 2 2 4 3 4 3 1 4 1 4 2 4 2 3 5 1 0 0 4 3 4 1 3 5 5 1 4 4 3 4 5 1 3 2 2 3 4 4 0 0 4 0 4 0 0 2 0 3 2 4 3 2 2 5 2 4 3 3 0 3 2 5 4 1 2 0 4 0 5 4 1 4 0 1 3 0 5 0 2 3 2 5 3 5 2 1 4 1 4 0 2 0 1 1 2 0 5 2 2 0 5 4 0 4 5 0 1 1 0 4 2 4 2 5 0 4 1 0 3 0 4 3 2 5 2 3 1 5 4 2 5 3 3 4 1 3 0 0 4 0 5 4 1 5 5 2 2 4 1 2 0 1 5 5 2 5 0 4 2 0 1 3 4 1 5 4 3 2 5 1 2 1 4 4 1 4 4 0 3 5 5 5 3 0 5 3 3 3 0 1 4 5 4 4 5 2 4 5 0 2 2 3 3 0 0 2 2 1 4 4 2 3 3 0 0 4 0 0 5 1 3 1 5 2 5 0 5 3 5 0 0 1 2 3 2 0 5 1 5 4 0 5 3 1 0 2 0 4 4 1 5 1 1 5 0 1 1 2 3 3 1 3 0 0 4 4 4 0 4 3 5 1 5 5 1 1 5 0 0 3 2 2 1 2 1 1 4 4 3 1 4 0 3 4 5 4 2 0 2 3 1 2 1 0 3 2 1 2 5 1 1 2 3 2 5 5 2 3 5 5 0 5 5 1 4 1 2 0 5 3 5 0 0 1 1 3 3 1 0 3 5 3 1 2 2 5 2 3 2 1 0 0 5 2 2 3 2 1 0 1 2 2 2 2 5 0 2 3 2 0 4 4 2 1 3 4 3 1 4 5 3 2 1 3 3 1 3 3 3 4 5 2 4 0 5 4 5 0 4 1 1 4 4 3 4 4 5 2 1 1 5 3 2 3 2 4 5 1 5 1 4 2 2 4 5 0 0 5 4 3 1 1 1 3 1 5 0 2 1 5 4 5 3 1 1 3 3 2 0 3 5 5 0 2 5 0 0 1 2 1 5 1 0 5 3 1 1 0 2 5 4 5 2 2 4 1 1 1 2 1 3 2 3 4 5 4 1 3 0 1 0 1 1 4 2 3 5 0 2 1 1 0 4 2 5 3 0 1 5 1 5 1 0 2 5 2 1 5 4 3 2 4 1 2 1 2 5 2 4 5 0 4 1 1 2 5 4 4 0 0 5 4 3 1 4 0 3 5 5 0 1 5 3 2 4 0 5 2 2 0 4 1 0 5 5 3 1 3 4 5 2 0 4 3 5 0 0 3 5 5 5 1 5 2 1 2 4 5 4 1 2 1 3 3 1 1 2 5 0 4 3 0 0 3 2 5 1 3 0 2 3 4 2 0 1 5 5 4 4 3 0 5 5 0 1 2 2 4 3 4 3 0 4 0 1 2 5 5 2 2 0 1 2 2 0 1 5 3 3 0 4 5 3 0 0 0 1 3 2 5 2 5 0 2 1 4 3 2 5 3 3 3 4 3 3 2 5 5 4 5 2 1 3 3 1 0 0 0 1 5 0 0 1 4 1 3 1 2 0 5 5 0 5 1 2 3 4 1 1 2 4 4 0 5 0 0 0 4 1 2 2 5 1 2 1 3 0 4 2 4 4 4 0 0 5 0 2 5 4 4 2 5 1 1 0 4 4 4 0 1 0 3 2 5 3 4 2 0 4 0 1 0 2 5 5 2 5 5 4 2 2 2 3 5 2 1 1 1 1 5 1 5 0 0 5 5 2 5 0 5 2 0 1 4 4 3 2 4 3 1 0 4 5 5 1 4 2 2 2 0 0 4 0 1 1 5 3 1 4 4 5 4 1 3 4 4 5 1 2 5 4 0 1 2 2 2 5 3 1 0 4 3 1 3 4 2 1 3 1 0 3 2 2 3 3 1 4 2 5 5 4 5 4 4 4 1 4 0 5 5 5 1 1 5 4 3 1 3 2 2 3 5 4 5 2 4 0 5 3 5 5 5 4 3 0 2 1 4 0 2 0 4 4 2 2 4 0 1 0 1 1 2 4 4 2 2 4 5 1 1 1 5 3 4 3 1 0 4 3 0 1 0 1 1 2 4 4 2 5 5 0 1 4 1 5 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5 3 2 4 3 3 3 1 0 5 1 5 3 5 3 4 4 4 3 0 2 2 2 0 5 5 5 0 1 3 0 3 1 2 0 2 0 1 1 5 5 4 4 0 0 1 2 5 4 5 1 1 2 5 4 0 2 4 0 3 1 0 4 0 5 4 5 1 5 1 0 5 4 4 1 3 4 5 3 4 3 4 3 4 4 5 2 5 0 0 4 5 4 4 5 2 3 0 5 4 0 2 0 3 4 3 0 3 5 2 1 3 3 5 5 3 2 1 2 2 3 0 2 1 0 1 2 3 1 5 1 5 4 0 1 3 0 5 0 1 4 5 3 1 4 3 5 4 1 4 4 3 1 4 3 2 5 3 4 2 1 1 3 1 2 2 0 2 0 4 0 0 1 5 0 3 0 4 3 2 1 2 1 1 5 3 3 0 4 5 4 4 4 2 5 0 0 4 3 5 5 2 2 5 4 2 1 1 4 1 5 0 4 2 1 4 3 5 0 5 4 2 5 1 5 4 0 1 4 3 0 0 4 1 4 2 1 3 2 2 4 1 1 3 5 5 1 5 1 3 2 4 2 2 1 5 0 4 1 2 3 5 5 4 0 3 3 1 3 1 4 1 2 1 1 2 4 4 0 1 1 3 4 2 1 2 2 1 0 0 1 1 2 4 1 3 5 5 3 3 1 5 3 4 0 3 4 5 5 3 1 0 4 2 5 1 5 3 5 1 0 1 3 4 2 5 1 4 4 3 1 2 0 0 0 3 3 5 0 3 5 0 3 2 5 0 3 3 5 2 4 5 4 2 1 3 4 1 3 3 2 1 2 4 1 0 5 4 0 1 3 0 5 5 0 5 3 5 4 3 2 1 2 4 3 5 1 4 3 0 0 4 4 3 0 5 4 3 0 0 5 0 0 0 1 1 3 3 0 3 1 0 0 3 2 4 3 0 1 3 5 4 2 0 1 2 1 4 3 2 5 3 0 3 5 2 0 3 5 4 0 4 3 0 4 0 4 3 4 2 0 1 2 0 0 3 2 1 1 1 1 2 2 2 2 0 5 4 4 1 1 0 5 0 5 5 0 2 4 0 2 1 4 5 3 1 0 5 4 0 2 1 2 2 5 2 1 4 3 5 3 5 1 0 0 3 5 1 5 3 0 0 0 2 0 1 3 4 5 0 0 3 1 0 2 4 1 1 4 5 0 0 1 5 0 4 3 0 3 0 4 2 1 3 0 3 0 4 5 2 1 3 1 5 1 3 4 2 4 4 5 3 3 0 1 4 5 2 4 0 2 4 0 4 1 4 5 4 5 4 3 2 4 5 3 5 1 3 5 2 2 1 1 2 1 3 5 1 2 0 5 2 2 2 5 0 1 2 4 4 5 1 4 2 3 3 1 0 5 1 2 4 5 1 4 2 3 3 0 1 0 0 4 1 3 5 2 5 4 5 1 1 4 2 0 4 3 2 5 1 2 2 4 0 3 1 3 4 5 4 4 3 4 5 3 3 0 4 1 0 1 4 3 3 2 4 1 0 2 0 5 2 1 0 4 3 4 4 5 0 4 3 2 5 2 4 2 0 3 2 0 5 0 4 3 4 4 5 4 4 0 0 0 5 5 2 1 3 2 2 2 0 5 1 3 5 4 4 4 2 1 4 3 5 3 4 0 3 3 3 4 4 3 2 0 2 2 4 1 5 0 3 1 5 1 1 5 5 0 0 3 1 3 4 1 3 1 4 1 2 3 5 3 1 4 2 1 4 1 1 5 5 4 1 4 4 5 5 2 4 5 2 3 1 0 4 0 4 2 1 5 3 1 2 1 4 2 2 0 0 2 0 2 2 2 5 4 3 5 4 4 0 1 0 4 2 1 2 4 1 2 3 4 0 0 0 2 3 0 1 5 5 1 0 0 1 4 0 0 2 5 5 2 4 3 2 0 5 4 4 3 3 0 4 2 1 4 1 3 5 1 4 1 3 3 3 1 2 2 4 1 5 2 2 5 4 4 2 1 2 2 4 0 5 5 1 1 0 4 3 5 2 3 1 1 1 3 2 0 4 5 4 2 4 5 1 5 5 1 3 5 0 2 3 0 1 1 5 3 0 2 5 5 2 5 4 1 1 3 0 4 3 3 4 5 4 2 5 0 4 2 1 4 4 2 5 3 3 5 1 3 3 0 4 3 2 2 4 5 4 5 0 2 1 1 5 3 5 0 0 2 3 2 1 1 0 5 1 3 5 1 5 0 3 3 4 4 4 0 1 0 0 0 3 1 3 3 0 4 3 4 5 0 3 0 4 1 1 5 0 5 4 1 2 4 4 0 2 1 4 5 5 0 2 3 1 3 3 2 3 0 3 3 5 2 1 0 5 3 1 3 2 2 4 5 1 3 2 5 5 2 0 2 4 5 0 2 5 1 3 0 5 1 5 5 4 5 5 2 0 3 1 3 1 5 5 5 3 2 5 0 0 5 1 3 5 3 0 0 1 1 2 2 1 0 0 0 0 4 1 2 0 4 5 3 5 0 4 1 2 4 4 4 3 2 4 4 4 4 2 4 5 4 5 2 4 1 1 0 3 3 2 5 0 4 4 2 1 4 5 4 4 2 4 5 5 2 0 3 1 1 5 1 5 4 4 4 4 2 1 4 0 4 5 3 5 4 1 1 0 4 0 0 0 0 4 5 4 3 5 0 0 4 2 3 3 0 2 3 5 0 1 0 0 3 2 3 5 2 1 3 3 4 5 2 3 2 4 0 1 1 3 5 2 0 4 5 1 1 0 1 4 2 4 0 2 0 0 0 2 1 5 0 4 3 0 2 5 0 4 2 5 0 5 4 4 0 0 5 2 4 2 0 1 1 5 2 1 0 5 3 5 2 5 0 3 2 3 1 3 0 0 5 4 2 1 3 4 5 5 4 4 0 3 3 3 1 1 1 4 5 1 0 1 3 1 4 2 2 0 5 3 5 0 2 1 5 1 3 5 2 0 4 2 5 5 1 5 1 0 5 2 3 2 1 2 5 2 3 1 4 3 2 1 3 0 0 1 3 5 3 0 4 3 0 0 5 1 0 2 5 5 4 0 4 0 3 2 4 4 2 5 5 5 3 4 4 2 0 1 2 5 1 3 2 5 0 5 3 4 4 2 3 2 1 0 1 1 4 3 0 3 0 3 0 0 1 3 3 3 5 4 5 4 0 2 5 0 5 3 3 4 0 4 2 5 3 0 3 1 3 4 0 4 1 5 3 3 1 4 2 1 3 0 5 2 1 3 0 1 0 3 2 2 5 3 4 0 3 3 4 5 5 2 5 2 0 5 3 3 5 3 3 3 1 2 5 1 3 3 0 4 1 0 3 4 5 5 5 1 0 5 0 2 4 0 2 3 1 1 0 4 5 0 4 0 5 4 3 3 3 3 4 5 5 4 4 1 4 0 4 1 4 2 5 2 1 4 5 5 1 4 0 4 4 5 2 0 2 1 2 0 4 5 2 4 3 5 0 4 0 2 3 2 0 3 1 0 2 1 5 3 3 4 3 3 1 4 4 4 1 1 0 0 0 0 5 4 4 1 2 3 1 1 4 4 2 5 3 3 0 5 4 2 5 4 3 2 4 3 1 4 2 5 1 5 3 4 5 2 1 3 2 1 2 2 4 4 0 2 0 0 4 2 5 0 5 0 3 3 4 2 3 0 3 5 1 1 4 3 0 0 1 2 4 1 4 2 1 1 0 4 4 3 1 0 0 1 3 5 1 3 3 3 4 4 3 3 2 3 5 0 2 2 0 1 3 4 1 0 3 0 0 0 1 0 4 0 3 3 0 4 3 3 1 2 3 0 5 5 3 3 4 3 5 3 5 5 1 2 5 0 2 1 3 0 2 1 5 2 2 4 3 3 1 3 3 4 0 1 4 4 3 0 1 0 4 2 2 0 5 4 4 2 3 2 3 0 1 1 3 1 1 2 3 5 2 1 3 2 5 5 0 2 2 5 3 5 4 1 3 2 3 2 4 1 1 2 3 4 5 4 4 3 0 5 4 0 3 0 2 5 2 2 4 2 1 4 4 3 0 =0 ≤1 ≥2 ≠0 ≥0 1 ≤4 =0 ≥3 ≠0 ≥0 4 =0 =0 ≤3 =0 ≥1 5 ≥0 ≤2 =0 ≥0 ≥1 1 ≥0 =0 ≤1 ≥0 ≠0 4 ≥0 =0 ≤1 ≥0 ≠0 2 ≤2 =0 ≥0 ≠0 ≥0 0 =0 ≤5 =0 ≥4 ≠0 1 ≤0 =0 ≥5 =0 ≠0 0 =0 ≤0 =0 ≥0 ≠0 4 ≤3 =0 ≥0 ≠0 ≥0 0 =0 ≤4 ≥2 =0 ≠0 3 ≥0 ≤2 =0 ≥3 ≠0 0 ≤2 =0 ≥1 =0 ≠0 1 =0 ≤1 ≥2 ≠0 =0 0 ≥0 ≤5 =0 ≥1 =0 3 =0 ≤0 =0 ≥4 ≠0 4 ≤2 =0 ≥5 =0 ≠0 4 =0 ≤3 =0 ≥2 ≠0 0 =0≤2 =0 ≥1 ≠0 5

Why are our results human competitive? Our evolved replication schemes (in 2D CA) and generic square calculations (in 1D CA) are equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal. (satisfying criterion B) Our best replication scheme Bidlo, 2016 Byl, 1989 IEEE Trans. On Evol. Computation (in print) Physica D: Nonlinear Phenomena, vol. 34, no. 1-2, pp. 295-299

Why are our results human competitive? Our evolved replication schemes (in 2D CA) and generic square calculations (in 1D CA) are equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal. (satisfying criterion B) Our best generic squaring CA some of our solutions for x=5 Wolfram, 2002 New Kind of Science (book), p. 638 Bidlo, 2016 IEEE Trans. On Evol. Computation (in print)

Why are our results human competitive? Our outcomes are publishable in its own right as a new scientific results independently of the fact that they were mechanically created because completely new algorithms were discovered using our method for the problems mentioned above, which exhibit better properties compared to existing solutions. (satisfying criterion D) Published in: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7377086&isnumber=4358751

Why are our results human competitive? In the author's opinion the proposed method solves a problem of indisputable difficulty in its field (i.e. automatic evolutionary design of multi-state cellular automata) because no similar results have yet been published using the existing approaches. (satisfying criterion G) Our experiments performed evolution of CA with up to 12 cell states, which theoretically allows more than 6.7 x 10268 534 transition functions. Example of an evolved moving GECCO label:

Why should this work win We believe that the proposed method, that provided human competitive results, can be generally applicable. Various benchmarks we have successfully solved: Generic squaring problem (1D) Replicating structures (2D CA) Pattern development problem the Czech flag (2D CA) Complex moving structures

Why should this work win We believe that the proposed method, that provided human competitive results, can be generally applicable. Examples of other benchmarks we have solved: A stable pattern development from a seed: the French flag A moving surname of the author developed from a 3-cell zygote CA is a platform potentially suitable for future technologies.

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