Consider an instance I to one-in-three-3sat and a satisfying assignment for I. We construct the collection QI of quartet trees, as well as the ternary phylogenetic tree Tσ as described in Sections 3 and 4, respectively. Clearly, constructing QI and …

Let k≥5 be an integer. Let G be a connected graph of girth at least k and x1,…,xk be terminals of G. Then one and only one of the following holds:

Let us start by fixing some notation. In a two-player game, let p be an efficiently computable correlated equilibrium that the players know and aim to generate. A typical scenario is that p is the lexicographically first correlated equilibrium that …

Pavlovian Population protocols are symmetric. We just proved that they have a very limited computational power. However, assuming population protocols symmetric (not-necessarily Pavlovian) is not truly a restriction.

We have compared three models of randomized strategies —behavioural, mixed, and general— in the context of graph games. Depending on the sub-case, we were able to expose variations in the amount of memory needed, the existence of finite-memory strat…

We conclude the paper with some open questions.

We proved that predicates on counts of input agents n≥0, n=0, n≥m, where n,m are some counts of input agents, can be computed by some Pavlovian population protocols.