Using a large empirical study of fuzzing (using AFL and libFuzzer), this paper explores the cost of finding vulnerabilities (or increasing coverage).
They produce some empirical laws:
Random fuzzers take exponentially more time to find each additional vulnerability. “Intuitively, when collecting baseball cards, the first couple of cards are easy to find, but collecting the next new card gets progressively more difficult.”
Finding the same vulnerabilities in half the time requires only half as many machines. “Intuitively, if each day you buy twice as many packs of baseball cards, you could have collected the same cards that you now have in half the time.”
These both assume zero cost for synchronization across fuzzers running in parallel. In an experiment with greybox fuzzers where the fuzzers shared their seeds as they discovered them and where they did not share seeds, they found that sharing significantly improved discovery rate.
They also produce mathematical models to help explain the patterns in their empirical data. A key part of those models is an assumption of a power-law distribution of bugs/features.
Their models are for purely random (blackbox) fuzzers but they suggest that, in the limit, graybox fuzzers turn into random fuzzers.