# Toward the Minimal Universal Petri Net

@article{Zaitsev2014TowardTM, title={Toward the Minimal Universal Petri Net}, author={Dmitry A. Zaitsev}, journal={IEEE Transactions on Systems, Man, and Cybernetics: Systems}, year={2014}, volume={44}, pages={47-58} }

A universal Petri net with 14 places, 42 transitions, and 218 arcs was built in the class of deterministic inhibitor Petri nets (DIPNs); it is based on the minimal Turing machine (TM) of Woods and Neary with 6 states, 4 symbols, and 23 instructions, directly simulated by a Petri net. Several techniques were developed, including bi-tag system (BTS) construction on a DIPN, special encoding of TM tape by two stacks, and concise subnets that implement arithmetic encoding operations. The simulation…

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## 25 Citations

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## References

SHOWING 1-10 OF 31 REFERENCES

Universal petri net

- Computer Science
- 2012

An algorithm using only 10 scalar nonnegative integer variables and executing an arbitrary inhibitor net is developed based on the state equation and is encoded by the universal inhibitor Petri net.

A New Synchronisation Model for Multi-Level Object Petri Nets

- Computer ScienceFundam. Informaticae
- 2004

An encoding of the proposed class of object Petrinets into linear logic Petri nets (LLPNs) is given, which directly leads to a specification that can be model-checked by existing tools.

Universal Inhibitor Petri Net

- Computer ScienceAWPN
- 2010

The universal inhibitor Petri net was constructed that executes an arbitrary given inhibitor PetRI net and was encoded as 10 scalar nonnegative integer numbers and represented by corresponding places of universal net.

An Axiomatization of the Token Game Based on Petri Algebras

- Mathematics, Computer ScienceFundam. Informaticae
- 2007

A class of residuated commutative monoids, called Petri algebras, are identified, for which one can mimic the token game of Petrinets to define the behaviour of generalized Petri nets whose flow relations and place contents are valued in such algebraic structures.

Petri Net Algebra

- Computer ScienceMonographs in Theoretical Computer Science An EATCS Series
- 2001

This book presents a step-by-step development of a rigorous framework for the specification and verification of concurrent systems. Petri Net Algebra takes its inspiration and methods from Process…

Deadlock Resolution in Automated Manufacturing Systems: A Novel Petri Net Approach

- Engineering
- 2009

Deadlock problems in flexible manufacturing systems (FMS) have received more and more attention in the last two decades. Petri nets are one of the more promising mathematical tools for tackling…

Petri nets: Properties, analysis and applications

- Computer Science
- 1989

The author proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis, and one section is devoted to marked graphs, the concurrent system model most amenable to analysis.

Petri nets for systems engineering - a guide to modeling, verification, and applications

- Computer Science
- 2003

The aim of the book is to illustrate progress in formal methods, based on Petri net formalisms, which contains a collection of examples arising from different fields, such as flexible manufacturing, telecommunication and workflow management systems.

Fault Diagnosis of Discrete-Event Systems Using Continuous Petri Nets

- Mathematics, Computer ScienceIEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans
- 2012

This paper defines three diagnosis states, namely N, U, and F, corresponding respectively to no fault, uncertain, and fault state, and proves that, given an observation, the resulting diagnosis state can be computed solving linear programming problems rather than integer programming problems as in the discrete case.

Translating robot programming language flow control into Petri nets

- Computer ScienceETFA2011
- 2011

This paper describes how structures for the flow control in robot programming languages can be translated into Petri nets, a common representation of robot programs that allows us to apply to them techniques originally developed for Petrinets.