Deciding low levels of tree-automata hierarchy

The paper discusses the hierarchy of indices of finite automata over infinite objects. This hierarchy corresponds exactly to the hierarchy of alternations of least and greatest fixpoints in the mu-calculus. It is also connected to quantifier hierarchies in monadic second-order logic. The open question is to find a procedure that given a regular tree language decides its level in the index hierarchy. Here, decision procedures are presented for low levels of the hierarchy. It is shown that these procedures have optimal complexity.

• Type: Journal
• Year: 2002
• Where: ENTCS
• Authors: Igor Walukiewicz
• Keywords: ENTCS 2002, Index Hierarchy, Monadic Second-order Logic, Procedures