The Non-deterministic Mostowski Hierarchy and Distance-Parity Automata

• Main Authors: Colcombet, Thomas, Löding, Christof
• Other Authors: Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Rheinisch-Westfälische Technische Hochschule Aachen (RWTH)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2008
• Subjects: Automata; Infinite trees; Fix-points; Mostowski; Rabin; [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]; Iceland
• Online Access: https://hal.archives-ouvertes.fr/hal-00347194; https://doi.org/10.1007/978-3-540-70583-3

International audience 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 $\omega+1$. The uniform universality problem consists in determining if this cost function is bounded by a finite value.