# What are the different notions of one-way functions?

For instance, A function that is computable but not invertable in log space, Is it one-way function?

What are the known definitions of one-way functions? (especially the ones that do not invoke polynomials)

A function '$f: {0, 1}^* \rightarrow {0, 1}^*$' is one-way if f can be computed by a polynomial time algorithm, but for every randomized polynomial time algorithm A,
$Pr[f(A(f(x))) = f(x)] < \frac{1}{p(n)}$
for every polynomial p(n) and sufficiently large n, assuming that x is chosen from the uniform distribution on ${0, 1}^n$ and the randomness of A.