Skip to main content
SpringerLink
Log in

Error-correcting Petri nets

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

The paper introduces error-correcting Petri nets, an algebraic methodology for designing synthetic biologic systems with monitoring capabilities. Linear error-correcting codes are used to extend the net’s structure in a way that allows for the algebraic detection and correction of non-reachable net markings. The presented methodology is based on modulo-p Hamming codes—which are optimal for the modulo-p correction of single errors—but also works with any other linear error-correcting code.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Adámek J (1991) Foundations of coding. Wiley, Chichester-New York

    MATH  Google Scholar 

  • de Lorenzo V et al (2006) Synthetic biology: challenges ahead. Bioinformatics 22(2):127–128

    Google Scholar 

  • Heinemann M, Panke S (2006) Synthetic biology—putting engineering into biology. Bioinformatics 22(22):2790–2799

    Google Scholar 

  • Mac Lane S, Birkoff G (1979) Algebra. MacMillan Publishing Co., Collier MacMillan Publishers, New York, London

    Google Scholar 

  • Mayr EV, Meyer AR (1981) The complexity of the final containment problem for Petri nets. J ACM, 3

  • Pagnoni A (1996) Detecting and correcting operation errors in distributed systems. Bull Eur Assoc Theoret Comput Sci 58

  • Rhee MY (1989) Error-correcting coding theory. McGraw-Hill, New York

    Google Scholar 

  • Reisig W, Rozenberg G (eds) (1989) Lectures on Petri nets I. Springer-Verlag, Berlin-Heidelberg

    Google Scholar 

  • van Lint JH (1992) Introduction to coding theory. Springer-Verlag, Berlin-Heidelberg

    MATH  Google Scholar 

Download references

Acknowledgements

The author thanks collegue and friend Monika Heiner for the motivation to write this paper, and for her insightful revision of it. Theorem 5 benefitted from her intervention particularly. The Petri nets in this paper have been drawn with Snoopy 2.0, courtesy of the Brandenburg University of Technology. Our thanks also go to two anonimous referees, who helped us with useful suggestions and necessary corrections. This work has been financially supported by FIRST (Fondo Italiano per la Ricerca Scientifica e Technologica).

Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, Milano, Italy

    Anastasia Pagnoni

Authors
  1. Anastasia Pagnoni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anastasia Pagnoni.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pagnoni, A. Error-correcting Petri nets. Nat Comput 10, 711–725 (2011). https://doi.org/10.1007/s11047-009-9150-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-009-9150-z

Keywords

Search

Navigation