I learned from this article that:
For real numbers, addition distributes over the maximum operation, and also over the minimum operation: $a+\max(b, c)=\max(a+b, a+c)$ and $a+\min(b, c)=min(a+b, a+c)$
I wonder if the following distributive law holds?
$\max(a, b)+\max(c, d)=\max(\max(a, b)+c, \max(a, b)+d)$ and $\min(a, b)+\min(c, d)=\min(\min(a, b)+c, \min(a, b)+d)$
I just replace a with $max(a, b)$.
I ask this question because I cannot get my head around while reading this paper: The Generalized Distributive Law, especially on the Viterbi part.
