Domain mu-calculus

The basic framework of domain mu-calculus was formulated in [39] more than ten years ago. This paper provides an improved formulation of a fragment of the mu-calculus without function space or powerdomain constructions, and studies some open problems related to this mu-calculus such as decidability and expressive power. A class of language equations is introduced for encoding mu-formulas in order to derive results related to decidability and expressive power of non-trivial fragments of the domain mu-calculus. The existence and uniqueness of solutions to this 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 equations using 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 to treat another fragment of the domain mu-calculus.