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Deciding the First Level of the $mu$-calculus Alternation Hierarchy (BibTeX)

@TECHREPORT{KuestersWilke-IFI-0209,
  author = {Ralf K{\"u}sters and Thomas Wilke},
  title = {{Deciding the First Level of the $\mu$-calculus Alternation Hierarchy}},
  institution = {Institut f{\"u}r Informatik und Praktische Mathematik, CAU Kiel, Germany},
  year = 2002,
  number = {0209},
  note = {Available from \url{http://www.informatik.uni-kiel.de/ifi/forschung/technische-berichte/}},
  abstract = {We show that the following problem is decidable and complete for deterministic exponential time. Given a formula of modal mu-calculus, determine if the formula is equivalent to a formula without greatest fixed point operators. In other words, we show that the first level of the mu-calculus fixed point alternation hierarchy is decidable in deterministic exponential time.}
}