  The power of fuzz testing lies in its random, often brute-force, generation
and execution of inputs to trigger unexpected behaviors and vulnerabilities in
software applications. However, given the reality of infinite possible input
sequences, pursuing all test combinations would not only be computationally
expensive, but practically impossible. Approximate Bayesian Computation (ABC),
a form of Bayesian simulation, represents a novel, probabilistic approach to
addressing this problem. The parameter space for working with these types of
problems is effectively infinite, and the application of these techniques is
untested in relevant literature. We use a relaxed, manual implementation of two
ABC methods, a Sequential Monte Carlo (SMC) simulation, and a Markov Chain
Monte Carlo (MCMC) simulation. We found promising results with the SMC
posterior and mixed results with MCMC posterior distributions on our white-box
fuzz-test function.
