DeNero and Klein 2010implicitly included these constraints in their representation: instead of sets of variables, they used a structured representation that only encodes triples (a, π, σ) satisfying both the mapping π = π(a) and the structural constraint that a can be generated by a block ITG grammar.
our inference procedure, BP, requires that we represent (a, π, σ) as an assignment of values to a set of variables.