DepLength is a calculator for the dependency length of sentences in English.

What is Dependency Length?

Considering the following sentences:

Four sentences along with their dependency representations. The number over each arc represents the length of the dependency in words. The total dependency length is given below each sentence. Sentences A and B have the same semantics, and either word order is acceptable in English; English speakers typically do not find one more natural than the other. Sentences C and D also both have the same semantics, but English speakers typically find C more natural than D.

Sentence A is a sequence of n words, where each word is a set of other words with the uniqueness property that if w∈x∈A and w∈y∈A then x=y . We can denote the k^th word in A as Ak. The sentence total dependency of a sentence A can be denoted:

[\sum_{k = 1}^{n}\sum_{w = A_{j} \in A_{k} }^{}\left |j - k \right |] 

where ϕ:A↦N satisfies ϕ(w)=d , where w=Aj , the unique superset of w is Ak , and |j−k|=d . More compactly, the sentence total dependency of a sentence A can be denoted