Then let τ be de- where True is any unary predicate that is always true for models in S. In this transduction, ϕ P b (x) is only true for input positions labeled b that do not follow another b; conversely, ϕ P c (x) is only true for input positions labeled b that do follow another b.
this allows us to use the usual conventions from strings: For an AR w, w n represents the AR consisting of n repetitions of w; w 0 is the empty AR whose tiers are both λ and thus has no association lines.