By combining concatenations of constant complexity with a strictly time-linear derivation order, the computational complexity degree of DBS (AIJ’01) is linear time (TCS’92). The only way to increase DBS complexity above linear would be a recursive ambiguity in the hear mode. In natural language, however, recursive ambiguity is prevented by grammatical disambiguation.
An example of grammatically disambiguating a nonrecursive ambiguity is the ‘garden path’ sentence The horse raced by the barn fell (Bever 1970). The continuation horse+raced introduces a local ambiguity between horse raced (active) and horse which was raced (passive), leading to two parallel derivation strands up to and including barn. Depending on continuing after barn with an interpunctuation or a verb, one of the [-global] readings (FoCL 11.3) is grammatically eliminated.
An example of grammatically disambiguating a recursive ambiguity is The man who loves the woman who loves Tom who Lucy loves, with the subordinating conjunction who. Depending on whether the continuation after who is a verb or a noun, one of the two [-global] readings is grammatically eliminated (momentary choice between who being subject or object).