Abstract
We study the complexity classes and through a semigroup ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. The semigroup is non-regular if and only if ≠ . The one-way functions considered here are based on worst-case complexity (they are not cryptographic); they are exactly the non-regular elements of . We prove various properties of , e.g. that it is finitely generated. We define reductions with respect to which certain universal one-way functions are -complete.