Natural limitations of decisions procedures for arithmetic with bounded quantifiers.
New recursive characterizations of the elementary functions and the functions computable in polynomial space.
We formulate recursive characterizations of the class of elementary functions and the class of functions computable in polynomial space that do not require any explicit bounded scheme. More specifically, we use functions where the input variables can occur in different kinds of positions ?normal and safe? in the vein of the Bellantoni and Cook's characterization of the polytime functions.
Nondeterminism is essential for reversal-bounded two-way multihead finite automata