The basic framework of domain μ-calculus was formulated in [39] more than ten years ago.This paper provides an improved formulation of a fragment of the μ-calculus without function space or powerdomain constructions,and studies some open problemsrelated to this μ-calculus such asdecidability and expressive power.A class of language equations is introducedfor encoding μ-formulas in order toderive results related to decidability and expressive power of non-trivial fragments of the domain μ-calculus.The existence and uniqueness of solutions tothis class of language equations constitute an important component of this approach.Our formulation is based on the recent work of Leiss [23], who established a sophisticated framework for solving language equationsusing Boolean automata(a.k.a. alternating automata [12,35]) and a generalized notion of language derivatives.Additionally, the early notion of even-linear grammars is adopted here totreat another fragment of the domain μ-calculus.
