The Non-deterministic Mostowski Hierarchy and Distance-Parity Automata

Given a Rabin tree-language and natural numbers i,j, the language is said to be i,j-feasible if it is accepted by a parity automaton using priorities {i,i+ 1,...,j}. The i,j-feasibility induces a hierarchy over the Rabin-tree languages called the Mostowski hierarchy. In this paper we prove that the problem of deciding if a language is i,j-feasible is reducible to the uniform universality problem for distance-parity automata. Distance-parity automata form a new model of automata extending both the nested distance desert automata introduced by Kirsten in his proof of decidability of the star-height problem, and parity automata over infinite trees. Distance-parity automata, instead of accepting a language, attach to each tree a cost in i¾?+ 1. The uniform universality problem consists in determining if this cost function is bounded by a finite value.

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