sequential dynamical systems
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Author(s):  
Juan A. Aledo ◽  
Luis G. Diaz ◽  
Silvia Martinez ◽  
Jose C. Valverde

2019 ◽  
Vol 97 (1-2) ◽  
pp. 467-481
Author(s):  
Juan A. Aledo ◽  
Luis G. Diaz ◽  
Silvia Martinez ◽  
Jose C. Valverde

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Juan A. Aledo ◽  
Luis G. Diaz ◽  
Silvia Martinez ◽  
Jose C. Valverde

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.


2018 ◽  
Vol 3 (2) ◽  
pp. 593-602 ◽  
Author(s):  
Juan A. Aledo ◽  
Luis G. Diaz ◽  
Silvia Martinez ◽  
Jose C. Valverde

AbstractIn this work, we deal with the predecessors existence problems in sequential dynamical systems over directed graphs. The results given in this paper extend those existing for such systems over undirected graphs. In particular, we solve the problems on the existence, uniqueness and coexistence of predecessors of any given state vector, characterizing the Garden-of-Eden states at the same time. We are also able to provide a bound for the number of predecessors and Garden-of-Eden state vectors of any of these systems.


2015 ◽  
Vol 36 (8) ◽  
pp. 2384-2407 ◽  
Author(s):  
ROMAIN AIMINO ◽  
JÉRÔME ROUSSEAU

We prove a concentration inequality for sequential dynamical systems of the unit interval enjoying an exponential loss of memory in the BV norm and we investigate several of its consequences. In particular, this covers compositions of$\unicode[STIX]{x1D6FD}$-transformations, with all$\unicode[STIX]{x1D6FD}$lying in a neighborhood of a fixed$\unicode[STIX]{x1D6FD}_{\star }>1$, and systems satisfying a covering-type assumption.


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