Elementary bounded languages

The POL be the class of polynomials having nonnegative integer coefficients and EXP the class of exponential functions. We call the closure of POL ∪ EXP under superposition, primitive recursion, and exponentiation, the class of elementary functions (EF). We have obtained that every elementary bounded language (i.e., language in the form {w1f1(n) ⋯ wtft(n | n ࢠ Nk, wi words fi ࢠ EF}) is context-sensitive. A concept for the computability of the functions usinggrammars is given, and it is shown that every function from EF is computable inthis manner, using context-sensitive grammars. By considering a new unaryoperation with respect to languages, called polynomial iteration (which is ageneralization of star closure) we prove that the class of context-sensitivelanguages is closed with respect to this operation but neither the class of contextfreenor the class of regular languages is closed