Outputs (36)

Graphs with minimum degree-entropy (2024)
Journal Article
Dong, Y., Gadouleau, M., Wan, P., & Zhang, S. (2024). Graphs with minimum degree-entropy. Information Sciences, 671, 120629. https://doi.org/10.1016/j.ins.2024.120629

We continue studying extremal values of the degree-entropy, which is an information-theoretic measure defined as the Shannon entropy based on the information functional involving vertex degrees. For a graph with a given number of vertices and edges a... Read More about Graphs with minimum degree-entropy.

Factorisation in the semiring of finite dynamical systems (2024)
Journal Article
Naquin, É., & Gadouleau, M. (2024). Factorisation in the semiring of finite dynamical systems. Theoretical Computer Science, 998, Article 114509. https://doi.org/10.1016/j.tcs.2024.114509

Finite dynamical systems (FDSs) are commonly used to model systems with a finite number of states that evolve deterministically and at discrete time steps. Considered up to isomorphism, those correspond to functional graphs. As such, FDSs have a sum... Read More about Factorisation in the semiring of finite dynamical systems.

Graphs with minimum fractional domatic number (2023)
Journal Article
Gadouleau, M., Harms, N., Mertzios, G. B., & Zamaraev, V. (2024). Graphs with minimum fractional domatic number. Discrete Applied Mathematics, 343, 140-148. https://doi.org/10.1016/j.dam.2023.10.020

The domatic number of a graph is the maximum number of vertex disjoint dominating sets that partition the vertex set of the graph. In this paper we consider the fractional variant of this notion. Graphs with fractional domatic number 1 are exactly th... Read More about Graphs with minimum fractional domatic number.

Bent functions in the partial spread class generated by linear recurring sequences (2022)
Journal Article
Gadouleau, M., Mariot, L., & Picek, S. (2023). Bent functions in the partial spread class generated by linear recurring sequences. Designs, Codes and Cryptography, 91(1), 63-82. https://doi.org/10.1007/s10623-022-01097-1

We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if their feedba... Read More about Bent functions in the partial spread class generated by linear recurring sequences.

Expansive automata networks (2020)
Journal Article
Bridoux, F., Gadouleau, M., & Theyssier, G. (2020). Expansive automata networks. Theoretical Computer Science, 843, 25-44. https://doi.org/10.1016/j.tcs.2020.06.019

An Automata Network is a map where Q is a finite alphabet. It can be viewed as a network of n entities, each holding a state from Q, and evolving according to a deterministic synchronous update rule in such a way that each entity only depends on its... Read More about Expansive automata networks.

Fixing monotone Boolean networks asynchronously (2020)
Journal Article
Aracena, J., Gadouleau, M., Richard, A., & Salinas, L. (2020). Fixing monotone Boolean networks asynchronously. Information and Computation, Article 104540. https://doi.org/10.1016/j.ic.2020.104540

The asynchronous automaton associated with a Boolean network f : f0; 1gn ! f0; 1gn is considered in many applications. It is the nite deterministic automaton with set of states f0; 1gn, alphabet f1; : : : ; ng, where the action of letter i on a state... Read More about Fixing monotone Boolean networks asynchronously.

Elementary, finite and linear vN-regular cellular automata (2020)
Journal Article
Castillo-Ramirez, A., & Gadouleau, M. (2020). Elementary, finite and linear vN-regular cellular automata. Information and Computation, 274, Article 104533. https://doi.org/10.1016/j.ic.2020.104533

Let G be a group and A a set. A cellular automaton (CA) over AG is von Neumann regular (vN-regular) if there exists a CA over AG such that = , and in such case, is called a weak generalised inverse of . In this paper, we investigate vN-regularity of... Read More about Elementary, finite and linear vN-regular cellular automata.

Complete Simulation of Automata Networks (2019)
Journal Article
Bridoux, F., Castillo-Ramirez, A., & Gadouleau, M. (2020). Complete Simulation of Automata Networks. Journal of Computer and System Sciences, 109, 1-21. https://doi.org/10.1016/j.jcss.2019.12.001

Consider a finite set A and . We study complete simulation of transformations of , also known as automata networks. For , a transformation of is n-complete of size m if it may simulate every transformation of by updating one register at a time. Using... Read More about Complete Simulation of Automata Networks.

On the stability and instability of finite dynamical systems with prescribed interaction graphs (2019)
Journal Article
Gadouleau, M. (2019). On the stability and instability of finite dynamical systems with prescribed interaction graphs. Electronic Journal of Combinatorics, 26(3), Article P3.32

The dynamical properties of finite dynamical systems (FDSs) have been investigated in the context of coding theoretic problems, such as network coding, and in the context of hat games, such as the guessing game and Winkler's hat game. The instability... Read More about On the stability and instability of finite dynamical systems with prescribed interaction graphs.

Max-flow min-cut theorems on dispersion and entropy measures for communication networks (2019)
Journal Article
Riis, S., & Gadouleau, M. (2019). Max-flow min-cut theorems on dispersion and entropy measures for communication networks. Information and Computation, 267, 49-73. https://doi.org/10.1016/j.ic.2019.03.004

The paper presents four distinct new ideas and results for communication networks: 1) We show that relay-networks (i.e. communication networks where different nodes use the same coding functions) can be used to model dynamic networks, in a way, vague... Read More about Max-flow min-cut theorems on dispersion and entropy measures for communication networks.