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In \cite{DeGroot}, DeGroot proposes a simple model of step by step opinion change under social influence. The model combines two types of matrices. Assuming a group of $n$ agents, a first $n\times n$ matrix represents the weighted influence network (who influences whom and how much), and a second $n \times m$ matrix represents the probability assigned by agents to $m$ different alternatives. Both the agents' opinion and the influence weights are taken within $[0,1]$ and are (row) stochastic (each row sums up to $1$). Given an opinion and an influence matrix, the opinion of each agent in the next time step is obtained through linear averaging.  In this paper we focus on the Boolean extreme of a DeGroot process. Opinions are defined over a BA structure, and hence are taken to be binary. Similarly, we take influence to be modeled by the binary case of an influence matrix. Influence is of an ``all-or-nothing'' type and each agent is therefore taken to be influenced by exactly one agent, possibly herself. The graph induced by such a binary influence matrix (called \emph{influence graph}) is therefore a structure $G = \tuple{\N, R}$ where $R \subseteq S^2$ \N^2$  is a binary relation which is serial ($\forall i\in \N, \exists j \in \N: i R j$) and functional ($\forall i,j,k \in \N$ if $i R j$ and $i R k$ then $j = k$). So each agent $i$ has exactly one successor (influencer or `guru') which we denote $R(i)$. An \emph{influence profile} $\G=(G_{p_1},\dots,G_{p_m})$ records how each agent is influenced by each other agent, with respect to each issue $p \in \Atoms$. Given a profile $\G$ the i$^{\mathit{th}}$ projection $\G_i$ denotes the influence graph for issue $p_i$. 
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Now fix an opinion profile $\O$ and an influence profile $\G$. Consider the stream $\O^0, \O^1, \ldots, \O^n, \ldots$ of opinion profiles recursively defined as follows:  \begin{itemize}  \item Base: $\O_0 := \O$  \item Step: for all $i \in \N$, $j\in \{1,...,m\}$,  $\O_i^{n+1}(p_j) := \O^{n}_{R_j(i)}(p_j)$. \end{itemize}  We call processes defined by the above dynamics \emph{Boolean DeGroot processes} (BDPs).  It should be clear that this dynamics is the extreme case of linear averaging applied on binary opinions and binary influence.