GADOULEAU , Maximilien

Can the interaction graph of a finite dynamical system force this system to have a ``complex'' dynamics ? In other words, given a finite interval of integers $A$, which are the signed digraphs $G$ such that every finite dynamical system $f:A^n\to A^n$ with $G$ as interaction graph has a ``complex'' dynamics ? If $|A|\geq 3$ we prove that no...

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 number of fixed points that only depends on $D$. We then discover relationships between the number of fixed...

Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the destinations can be simultaneously satisfied by using linear network coding. The guessing number approach...

International audience

The asynchronous automaton associated with a Boolean network f : {0, 1} n → {0, 1} n is considered in many applications. It is the finite deterministic automaton with set of states {0, 1} n , alphabet {1,. .. , n}, where the action of letter i on a state x consists in either switching the ith component if f i (x) = x i or doing nothing...

We investigate sets of Mutually Orthogonal Latin Squares (MOLS) generated by Cellular Automata (CA) over finite fields. After introducing how a CA defined by a bipermutive local rule of diameter $d$ over an alphabet of $q$ elements generates a Latin square of order $q^{d-1}$, we study the conditions under which two CA generate a pair of...