The disclosure relates to various distance metrics that may quantify semantic and syntactic relationships between devices. More particularly, a first grammar associated with a first device and a second grammar associated with a second device may each comprise a symbol sequence that re-expresses one or more sequenced data items and one or more rules that represent a repeated pattern in the symbol sequence. Accordingly, one or more distance metrics that quantify a similarity between the first grammar and the second grammar may be calculated according to a comparison between the rules in the first grammar and the rules in the second grammar such that a relationship between the first device and the second device can be determined according to the one or more distance metrics.