Outputs (5)

Lengths of words in transformation semigroups generated by digraphs (2016)
Journal Article
Cameron, P. J., Castillo-Ramirez, A., Gadouleau, M., & Mitchell, J. D. (2017). Lengths of words in transformation semigroups generated by digraphs. Journal of Algebraic Combinatorics, 45(1), 149-170. https://doi.org/10.1007/s10801-016-0703-9

Given a simple digraph D on n vertices (with n≥2n≥2 ), there is a natural construction of a semigroup of transformations ⟨D⟩⟨D⟩ . For any edge (a, b) of D, let a→ba→b be the idempotent of rank n−1n−1 mapping a to b and fixing all vertices other than... Read More about Lengths of words in transformation semigroups generated by digraphs.

On Finite Monoids of Cellular Automata (2016)
Presentation / Conference Contribution
Castillo-Ramirez, A., & Gadouleau, M. (2016, June). On Finite Monoids of Cellular Automata. Presented at International workshop on cellular automata and discrete complex systems, Zurich, Switzerland

For any group G and set A, a cellular automaton over G and A is a transformation τ:AG→AGτ:AG→AG defined via a finite neighbourhood S⊆GS⊆G (called a memory set of ττ) and a local function μ:AS→Aμ:AS→A. In this paper, we assume that G and A are both fi... Read More about On Finite Monoids of Cellular Automata.

Reduction and Fixed Points of Boolean Networks and Linear Network Coding Solvability (2016)
Journal Article
Gadouleau, M., Richard, A., & Fanchon, E. (2016). Reduction and Fixed Points of Boolean Networks and Linear Network Coding Solvability. IEEE Transactions on Information Theory, 62(5), 2504-2519. https://doi.org/10.1109/tit.2016.2544344

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 destination... Read More about Reduction and Fixed Points of Boolean Networks and Linear Network Coding Solvability.

Simple dynamics on graphs (2016)
Journal Article
Gadouleau, M., & Richard, A. (2016). Simple dynamics on graphs. Theoretical Computer Science, 628, 62-77. https://doi.org/10.1016/j.tcs.2016.03.013

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:An→An with G as in... Read More about Simple dynamics on graphs.

Ranks of finite semigroups of one-dimensional cellular automata (2016)
Journal Article
Castillo-Ramirez, A., & Gadouleau, M. (2016). Ranks of finite semigroups of one-dimensional cellular automata. Semigroup Forum, 93(2), 347-362. https://doi.org/10.1007/s00233-016-9783-z

Since first introduced by John von Neumann, the notion of cellular automaton has grown into a key concept in computer science, physics and theoretical biology. In its classical setting, a cellular automaton is a transformation of the set of all confi... Read More about Ranks of finite semigroups of one-dimensional cellular automata.