A decision procedure for alternation-free modal µ-calculi

The alternation-free fragment of the propositional modal μ-calculus (AFμ) allows less complex decision procedure for satisfiability judgment than the full μ-calculus, yet it still has strong expressive power. In this paper, we present a concrete decision procedure with its complexity for AFμ enriched by features of nominals, backward modalities, and functional modalities. While AFμ with all three features is undecidable, AFμ with two out of the three features are decidable and the procedure is sound and complete for these combinations. The procedure is suitable for implementation with BDDs. An application of the decision procedure for shape analysis is also reported.