Nonnegative Positionality in Regular Abstract NumerationSystems: Balance-Loop Normal Forms and Viability Filtrations

Let L ⊆ {0, 1, , c}* be an infinite regular language, ordered genealogically, and let GL(w) denote the genealogical rank of w ∈ L. We ask whether there exists a sequence of nonnegative integer weights U = (Un)n≥0 such that GL(a1⋯am) = ∑i=1m aiUm−i (a1⋯am ∈ L). The companion paper [5, Theorem 6.1] proves [ ] The post Nonnegative Positionality in Regular Abstract NumerationSystems: Balance-Loop…