BC-ε: A Recursion-Theoretic Characterization of LOGSPACE

We present BC ε which is a function algebra that is sound and complete for LOGSPACE. It is based on the novel recursion-theoretic principle of generalized recursion where the step length of primitive recursion can be varied at each step. This allows elegant representations of functions like logarithm and division. Unlike characterizations found in the literature, it is noticeable that there does not appear to be a way to represent pairs in the algebra. The soundness proof uses a simulation based on “computational amnesia” where, analogously to tail recursion optimization, a recursive call replaces its own activation record. Even though the call is not necessarily tail, we recover the full recursion by repeatedly restarting the computation.