Related papers: Synchronizing Boolean networks asynchronously
We have improved an algorithm generating synchronizing automata with a large length of the shortest reset words. This has been done by refining some known results concerning bounds on the reset length. Our improvements make possible to…
A coloring of a digraph with a fixed out-degree k is a distribution of k labels over the edges resulting in a deterministic finite automaton. An automaton is called synchronizing if there exists a word which sends all states of the…
We present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. These automata are closely related to primitive digraphs with large exponent.
Boolean Networks (BNs) describe the time evolution of binary states using logic functions on the nodes of a network. They are fundamental models for complex discrete dynamical systems, with applications in various areas of science and…
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
This paper considers the existence of short synchronizing words in deterministic finite automata (DFAs). We define two general strategies for generating synchronizing words, and we show that each of these strategies can be applied if and…
Most slowly synchronizing automata over binary alphabets are circular, i.e., containing a letter permuting the states in a single cycle, and their set of synchronizing words has maximal state complexity, which also implies complete…
We are interested in the relationships between the number fixed points in a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$ and its interaction graph, which is the arc-signed digraph $G$ on $\{1,\dots,n\}$ that describes the positive and negative…
We study synchronizing automata with the shortest reset words of relatively large length. First, we refine the Frankl-Pin result on the length of the shortest words of rank $m$, and the B\'eal, Berlinkov, Perrin, and Steinberg results on…
A word $s$ of letters on edges of underlying graph $\Gamma$ of deterministic finite automaton (DFA) is called synchronizing if $s$ sends all states of the automaton to a unique state. J. \v{C}erny discovered in 1964 a sequence of $n$-state…
We prove that a random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs). Moreover, we also prove that the…
In this paper, we are interested in the number of fixed points of functions $f:A^n\to A^n$ over a finite alphabet $A$ defined on a given signed digraph $D$. We first use techniques from network coding to derive some lower bounds on the…
Frame synchronization is the act of discerning the first bit of a valid data frame inside an incoming transmission. This is particularly important in high-noise environments where the communication channel significantly alters transmitted…
Synchronizing words in classical automata theory provide a mechanism to reset any state of a deterministic automaton to a specific target state via a carefully chosen finite sequence of transition rules. In this work, we extend the concept…
In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far…
In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite…
We show that synchronism can significantly impact on network behaviours, in particular by filtering unstable attractors induced by a constraint of asynchronism. We investigate and classify the different possible impacts that an addition of…
In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are…
It is known, that an $\epsilon$-machine is either exactly or asymptotically synchronizing. In the exact case, the observer can infer the current machine state after observing $L$ generated symbols with probability $1-a^L$ where $0 \leq a<1$…
We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2^n states, where n is the maximal length of words…