International Conference on Machines, Computations, and Universality

MCU 2015: Machines, Computations, and Universality pp 180-197

Universality in Infinite Petri Nets

Conference paper

DOI: 10.1007/978-3-319-23111-2_12

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9288)
Cite this paper as:
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

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.

Keywords

Universal Petri net Infinite Petri net Linear cellular automaton Turing machine Simulation Complexity 

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Computer ScienceVistula UniversityWarsawPoland

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