@INPROCEEDINGS{KuestersWilke-FSTTCS-2002, author = {Ralf K{\"u}sters and Thomas Wilke}, title = {{Deciding the First Level of the $\mu$-calculus Alternation Hierarchy}}, booktitle = {FSTTCS 2002: Foundations of Software Technology and Theoretical Computer Science --- 22nd Conference}, pages = {241--252}, year = 2002, editor = {M.~Agrawal and A.~Seth}, volume = 2556, series = {Lecture Notes in Computer Science}, publisher = {Springer-Verlag}, 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.} }