Inproceedings: An article in a conference proceedings.
Linear Game Automata: Decidable Hierarchy Problems for Stripped-Down Alternating Tree Automata
Title of the conference
Computer Science Logic: 23rd International Workshop, CSL 2009, 18th Annual Conference of the EACSL, Coimbra, Portugal, September 7-11, 2009, Proceedings
Grädel E., Kahle R.
Lecture Notes in Computer Science
For deterministic tree automata, classical hierarchies, like Mostowski-Rabin (or index) hierarchy, Borel hierarchy, or Wadge hierarchy, are known to be decidable. However, when it comes to non-deterministic tree automata, none of these hierarchies is even close to be understood. Here we make an attempt in paving the way towards a clear understanding of tree automata. We concentrate on the class of linear game automata (LGA), and prove within this new context, that all corresponding hierarchies mentioned above—Mostowski-Rabin, Borel, and Wadge—are decidable. The class LGA is obtained by taking linear tree automata with alternation restricted to the choice of path in the input tree. Despite their simplicity, LGA recognize sets of arbitrary high Borel rank. The actual richness of LGA is revealed by the height of their Wadge hierarchy: (ω^ω)^ω.
Linear tree automata, Wadge Hierarchy, Index Problem, Borel Hierarchy
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