On the Complexity of Set - Based Analysis ( 1288 . 232 )

We formally deene the set-based abstraction of any language whose operational semantics can be deened by environment evaluation. The Aiken-Wimmers soft type system precisely corresponds to this set-based abstraction under their operational semantics. The Heintze set-based analysis is precisely this set-based abstraction under a diierent operational semantics. In general, set-based abstraction determines a notion of SBA-safety. Aiken-Wimmers typability is a form of SBA-safety. SBA-safety is decidable in most cases. For monovariant functional programs with shallow case statements SBA-safety is decidable in O(n 3) time under any standard operational semantics. We show here that if we allow deep patterns in the case statements of monovariant functional programs the problem of determining SBA-safety becomes complete for deterministic exponential time (under any standard operational semantics). We also systematically characterize the complexity of determining SBA-safety for monovariant programs as a function of the semantics and syntactic complexity of case statements.