discusses an extension of DCG in order to analyze the Australian free word-order language `Guugu Yimidhirr'. In ordinary DCG a category is associated with a pair indicating which location the constituent occupies. Johnson proposes that constituents in the extended version of DCG be associated with a set of such pairs. A constituent thus `occupies' a set of continuous locations. The following is a sentence of Guugu Yimidhirr:
In this sentence, the discontinuous constituent `Yarraga-aga-mu-n ...biiba-ngun' (boy's father) is associated with the set of locations:
Johnson notices that such expressions can be represented with bit vectors. In a grammar rule the sets of locations of the daughters of the rule are `combined' to construct the set of locations associated with the mother node. The predicate combines(s1, s2, s) is true iff s is equal to the (bit-wise) union of s1 and s2, and the (bit-wise) intersection of s1 and s2 is null (ie. s1 and s2 must be non-overlapping locations). Grammars which exclusively use this predicate, are permutation-closed. For Guugu Yimidhirr Johnson also proposes a concatenative rule for possessive noun constructions in which the possessive is identified by position rather than by inflectional markings. Apart from these constructions Guugu Yimidhirr is said to be permutation-closed (Johnson, quoting ). Earley deduction  is used as a general proof procedure for such extended DCG grammars.