Solution to the predecessors and Gardens-of-Eden problems for synchronous systems over directed graphs

Juan A. Aledo, Luis G. Diaz, Silvia Martinez and Jose C. Valverde

Applied Mathematics and Computation, 2019, vol. 347, issue C, 22-28

Abstract: In this work, we give a solution to the predecessors problems for synchronous systems over directed graphs, so extending the results given for systems over undirected graphs. In this same sense, we provide a characterization to have at least one predecessor for any given state and, consequently, a characterization of the Garden-of-Eden states. Furthermore, we solve the unique predecessor problem, the coexistence of predecessors problem and the number of predecessors problem, providing the best bounds for such a number and for the number of Garden-of-Eden states.

Keywords: Parallel dynamical systems; Boolean functions; Predecessors; Garden-of-Eden points (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318309512
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:22-28

DOI: 10.1016/j.amc.2018.10.077

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().