6 papers
Injective and pseudo-injective polynomial equations: From permutations to dynamical systems
Antonio E. Porreca, Marius Rolland
We study the computational complexity of decomposing finite discrete dynamical systems (FDDSs) in terms of the semiring operations of alternative and synchronous execution, which i…
Non-trivial automata networks do exist that solve the global majority problem with the local majority rule
Pedro Paulo Balbi, Kévin Perrot, Marius Rolland +1
The global majority problem, often referred to as the Density Classification Task, is a classical benchmark in the context of probing the computational capabilities of automata net…
Majority Boolean networks classifying density: structural characterization and complexity
Kévin Perrot, Marius Rolland
Given a set of entities each holding a Boolean state, the Density Classification Task (DCT) asks them to converge to the most represented state. Given a directed graph of entities…
Solving "pseudo-injective" polynomial equations over finite dynamical systems
Antonio E. Porreca, Marius Rolland
We consider the semiring of abstract finite dynamical systems up to isomorphism, with the operations of alternative and synchronous execution. We continue searching for efficient a…
Injectivity of polynomials over finite discrete dynamical systems
Antonio E. Porreca, Marius Rolland
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the…
Roots in the semiring of finite deterministic dynamical systems
François Doré, Kévin Perrot, Antonio E. Porreca +2
Finite discrete-time dynamical systems (FDDS) model phenomena that evolve deterministically in discrete time. It is possible to define sum and product operations on these systems (…