A one-way function is a function that is easy to compute but hard to invert* on average*. We
establish the first characterization of a one-way function by* worst-case* hardness …

We show broad equivalences in the average-case complexity of many different meta-
complexity problems, including Kolmogorov complexity, time-bounded Kolmogorov …

Whether one-way functions (OWF) exist is arguably the most important problem in
Cryptography, and beyond. While lots of candidate constructions of one-way functions are …

A long-standing and central open question in the theory of average-case complexity is to
base average-case hardness of NP on worst-case hardness of NP. A frontier question along …

Pessiland is one of Impagliazzo's five possible worlds in which NP is hard on average, yet
no one-way function exists. This world is considered the most pessimistic because it offers …

Understanding the relationship between the worst-case and average-case complexities of
NP and of other subclasses of PH is a long-standing problem in complexity theory. Over the …

Symmetry of Information (SoI) is a fundamental property of Kolmogorov complexity that
relates the complexity of a pair of strings and their conditional complexities. Understanding if …

The classical coding theorem in Kolmogorov complexity states that if an $ n $-bit string $ x $
is sampled with probability $\delta $ by an algorithm with prefix-free domain then K …

A PAC learning model involves two worst-case requirements: a learner must learn all
functions in a class on all example distributions. However, basing the hardness of learning …

Symmetry of information for time-bounded Kolmogorov complexity is a hypothetical
inequality that relates time-bounded Kolmogorov complexity and its conditional analogue. In …