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Domain mu-calculus

Published online by Cambridge University Press:  15 January 2004

Guo-Qiang Zhang
Guo-Qiang Zhang*
Affiliation:
Department of Electrical Engineering and Computer Science, Case Western Reserve University, Cleveland, OH 44106, USA.; gqz@eecs.cwru.edu.
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Abstract

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.

Keywords

Domain theorymu-calculusformal languagesBoolean automata.

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