Computing in Logarithmic Space

Abstract

The set logspace, of logarithmic space computable string functions is defined. It is easily seen that logspace ≤ polytime, the set of polynomial time computable functions. ogspace is shown to equal L, the smallest class of recursive string functions containing concatenation and the equality function, and closed under explicit transformation, substitution of a function for a variable and two restricted types of recursion on notation. The first is called recursion of concatenation and only allows top level concetenation of the value of the recursive call. The second, called log bounded recursion on notation, will only define string functions whose length is bounded by 0(log n) on arguments of length n. Some additional closure properties of logspace are also described.