The Non-deterministic Mostowski Hierarchy and Distance-Parity Automata
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...
Main Authors: | , |
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Other Authors: | , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2008
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Subjects: | |
Online Access: | https://hal.science/hal-00347194 https://doi.org/10.1007/978-3-540-70583-3 |
Summary: | 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. |
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