Universality in Infinite Petri Nets

Finite classical Petri nets are non-Turing-complete. Two infi- nite Petri nets are constructed which simulate the linear cellular automa- ton Rule 110 via expanding traversals of the cell array. One net is obtained via direct simulation of the cellular automaton while the other net simulates a Turing machine, which simulates the cellular automa- ton. They use cell models of 21 and 14 nodes, respectively, and simulate the cellular automaton in polynomial time. Based on known results we conclude that these Petri nets are Turing-complete and run in polyno- mial time. We employ an induction proof technique that is applicable for the formal proof of Rule 110 ether and gliders properties further to the constructs presented by Matthew Cook.

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