U. of California, Berkeley
Program analysis and verification are provably hard, and we have all learned not to expect perfect results. We are accustomed to pay this cost in terms of completeness and algorithm complexity. Recently we have started to investigate what benefits we could expect if we are willing to trade off minuscule amounts of soundness. This talk will describe a number of randomized analysis algorithms which are much simpler, and in many cases have lower computational complexity, than the corresponding deterministic algorithms. The price paid is that such algorithms may, in rare occasions, infer properties that are not true. We will describe both the intuitions and the technical arguments that allow us to evaluate and control the probability that an erroneous result is returned, in terms of various parameters of the algorithm. These arguments will also shed light on the limitations of such randomized algorithms.
These randomized algorithms were developed initially for program analysis, but have applications in automated deduction as well. We will describe a satisfiability procedure for uninterpreted functions and linear arithmetic, and compare it experimentally with deterministic algorithms. We will also show that it is possible to integrate symbolic and randomized techniques to leverage the benefits of both worlds. In this class, we will show extensions of randomized algorithms to inter-procedural analyses, and an integration of boolean decision diagrams with linear arithmetic and uninterpreted functions.