IDEAS home Printed from https://ideas.repec.org/a/hin/complx/6280960.html
   My bibliography  Save this article

Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems

Author

Listed:
  • Juan A. Aledo
  • Luis G. Diaz
  • Silvia Martinez
  • Jose C. Valverde

Abstract

In this paper, we deal with one of the main computational questions in network models: the predecessor-existence problems. In particular, we solve algebraically such problems in sequential dynamical systems on maxterm and minterm Boolean functions. We also provide a description of the Garden-of-Eden configurations of any system, giving the best upper bound for the number of Garden-of-Eden points.

Suggested Citation

  • Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2019. "Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems," Complexity, Hindawi, vol. 2019, pages 1-10, March.
    • Handle: RePEc:hin:complx:6280960
    DOI: 10.1155/2019/6280960
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/6280960.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/6280960.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/6280960?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Juan A. Aledo & Silvia Martinez & Jose C. Valverde, 2015. "Parallel Dynamical Systems over Graphs and Related Topics: A Survey," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-14, March.
    2. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2017. "On the Periods of Parallel Dynamical Systems," Complexity, Hindawi, vol. 2017, pages 1-6, January.
    3. G. Chiaselotti & G. Marino & P. A. Oliverio & D. Petrassi, 2013. "A Discrete Dynamical Model of Signed Partitions," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, April.
    4. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Solution to the predecessors and Gardens-of-Eden problems for synchronous systems over directed graphs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 22-28.
    5. Barrett, Chris L & Chen, William Y.C & Zheng, Michelle J, 2004. "Discrete dynamical systems on graphs and Boolean functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 487-497.
    6. Chiaselotti, G. & Gentile, T. & Oliverio, P.A., 2014. "Parallel and sequential dynamics of two discrete models of signed integer partitions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1249-1261.
    7. Toroczkai, Zoltán & Guclu, Hasan, 2007. "Proximity networks and epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(1), pages 68-75.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2020. "Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    2. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Dynamical attraction in parallel network models," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 874-888.
    3. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2017. "On the Periods of Parallel Dynamical Systems," Complexity, Hindawi, vol. 2017, pages 1-6, January.
    4. Juan A. Aledo & Ali Barzanouni & Ghazaleh Malekbala & Leila Sharifan & Jose C. Valverde, 2020. "On the Periodic Structure of Parallel Dynamical Systems on Generalized Independent Boolean Functions," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    5. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Solution to the predecessors and Gardens-of-Eden problems for synchronous systems over directed graphs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 22-28.
    6. Mauro Mezzini & Fernando L. Pelayo, 2020. "An Algorithm for Counting the Fixed Point Orbits of an AND-OR Dynamical System with Symmetric Positive Dependency Graph," Mathematics, MDPI, vol. 8(9), pages 1-9, September.
    7. Sanahuja, Silvia M., 2016. "New rough approximations for n-cycles and n-paths," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 96-108.
    8. Christensen, Claire & Albert, István & Grenfell, Bryan & Albert, Réka, 2010. "Disease dynamics in a dynamic social network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2663-2674.
    9. Sascha Holzhauer & Friedrich Krebs & Andreas Ernst, 2013. "Considering baseline homophily when generating spatial social networks for agent-based modelling," Computational and Mathematical Organization Theory, Springer, vol. 19(2), pages 128-150, June.
    10. Sara D. Cardell & Amparo Fúster-Sabater, 2019. "Binomial Representation of Cryptographic Binary Sequences and Its Relation to Cellular Automata," Complexity, Hindawi, vol. 2019, pages 1-13, March.
    11. Xie He & Amir Ghasemian & Eun Lee & Aaron Clauset & Peter J. Mucha, 2024. "Sequential stacking link prediction algorithms for temporal networks," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    12. Chiaselotti, G. & Gentile, T. & Infusino, F. & Oliverio, P.A., 2018. "Dependency and accuracy measures for directed graphs," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 781-794.
    13. Xiaoyan Zhang & Chao Wang, 2019. "Solutions to All-Colors Problem on Graph Cellular Automata," Complexity, Hindawi, vol. 2019, pages 1-11, June.
    14. Hegemann, Rachel A. & Smith, Laura M. & Barbaro, Alethea B.T. & Bertozzi, Andrea L. & Reid, Shannon E. & Tita, George E., 2011. "Geographical influences of an emerging network of gang rivalries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3894-3914.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:6280960. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.