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Universality in Infinite Petri Nets

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Machines, Computations, and Universality (MCU 2015)

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Abstract

Finite classical Petri nets are non-Turing-complete. Two infinite Petri nets are constructed which simulate the linear cellular automaton 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 automaton. 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 polynomial 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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Acknowledgement

The author would like to thank reviewers whose comments allowed the refinement of the presentation and Jacob Hendricks for his help in improving the readability of the paper.

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Correspondence to Dmitry A. Zaitsev .

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Zaitsev, D.A. (2015). Universality in Infinite Petri Nets. In: Durand-Lose, J., Nagy, B. (eds) Machines, Computations, and Universality. MCU 2015. Lecture Notes in Computer Science(), vol 9288. Springer, Cham. https://doi.org/10.1007/978-3-319-23111-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-23111-2_12

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