  In order to successfully model Long Distance Dependencies (LDDs) it is
necessary to understand the full-range of the characteristics of the LDDs
exhibited in a target dataset. In this paper, we use Strictly k-Piecewise
languages to generate datasets with various properties. We then compute the
characteristics of the LDDs in these datasets using mutual information and
analyze the impact of factors such as (i) k, (ii) length of LDDs, (iii)
vocabulary size, (iv) forbidden subsequences, and (v) dataset size. This
analysis reveal that the number of interacting elements in a dependency is an
important characteristic of LDDs. This leads us to the challenge of modelling
multi-element long-distance dependencies. Our results suggest that attention
mechanisms in neural networks may aide in modeling datasets with multi-element
long-distance dependencies. However, we conclude that there is a need to
develop more efficient attention mechanisms to address this issue.
