The complexity of monadic recursion schemes: exponential time bounds

Abstract

We study the computational complexity of decision problems for the class M of monadic recursion schemes. By the “executability problem” for a class 't of monadic recursion schemes, we mean the problem of determining whether a given defined function symbol of a given scheme in .'t can be called during at least one computation. The executability problem for a class I of very simple monadic recursion schemes is shown to require deterministic exponential time. Using arguments about executability problems and about the class I , a number of decision problems for. M and for several of. M 's subclasses are shown to require deterministic exponential time. Deterministic exponential time upper bounds are also presented for several of these decision problems.