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 ω+1. The uniform universality problem consists in determining if this cost function is bounded by a finite value. © 2008 Springer-Verlag.
CITATION STYLE
Colcombet, T., & Löding, C. (2008). The non-deterministic Mostowski hierarchy and distance-parity automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5126 LNCS, pp. 398–409). https://doi.org/10.1007/978-3-540-70583-3_33
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