Predicting SMT solver performance for software verification

The approach Why3 takes to interfacing with a wide variety of interactive and automatic theorem provers works well: it is designed to overcome limitations on what can be proved by a system which relies on a single tightly-integrated solver. In common with other systems, however, the degree to which proof obligations (or “goals”) are proved depends as much on the SMT solver as the properties of the goal itself. In this work, we present a method to use syntactic analysis to characterise goals and predict the most appropriate solver via machine-learning techniques. Combining solvers in this way - a portfolio-solving approach - maximises the number of goals which can be proved. The driver-based architecture of Why3 presents a unique opportunity to use a portfolio of SMT solvers for software verification. The intelligent scheduling of solvers minimises the time it takes to prove these goals by avoiding solvers which return Timeout and Unknown responses. We assess the suitability of a number of machinelearning algorithms for this scheduling task. The performance of our tool Where4 is evaluated on a dataset of proof obligations. We compare Where4 to a range of SMT solvers and theoretical scheduling strategies. We find that Where4 can out-perform individual solvers by proving a greater number of goals in a shorter average time. Furthermore, Where4 can integrate into a Why3 user’s normal workflow - simplifying and automating the non-expert use of SMT solvers for software verification

Predicting SMT solver performance for software verification

The approach Why3 takes to interfacing with a wide variety of interactive and automatic theorem provers works well: it is designed to overcome limitations on what can be proved by a system which relies on a single tightly-integrated solver. In common with other systems, however, the degree to which proof obligations (or “goals”) are proved depends as much on the SMT solver as the properties of the goal itself. In this work, we present a method to use syntactic analysis to characterise goals and predict the most appropriate solver via machine-learning techniques. Combining solvers in this way - a portfolio-solving approach - maximises the number of goals which can be proved. The driver-based architecture of Why3 presents a unique opportunity to use a portfolio of SMT solvers for software verification. The intelligent scheduling of solvers minimises the time it takes to prove these goals by avoiding solvers which return Timeout and Unknown responses. We assess the suitability of a number of machinelearning algorithms for this scheduling task. The performance of our tool Where4 is evaluated on a dataset of proof obligations. We compare Where4 to a range of SMT solvers and theoretical scheduling strategies. We find that Where4 can out-perform individual solvers by proving a greater number of goals in a shorter average time. Furthermore, Where4 can integrate into a Why3 user’s normal workflow - simplifying and automating the non-expert use of SMT solvers for software verification

A Unified View of Piecewise Linear Neural Network Verification

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and the theoretical hardness of proving their properties, researchers have been successful in verifying some classes of models by exploiting their piecewise linear structure and taking insights from formal methods such as Satisifiability Modulo Theory. These methods are however still far from scaling to realistic neural networks. To facilitate progress on this crucial area, we make two key contributions. First, we present a unified framework that encompasses previous methods. This analysis results in the identification of new methods that combine the strengths of multiple existing approaches, accomplishing a speedup of two orders of magnitude compared to the previous state of the art. Second, we propose a new data set of benchmarks which includes a collection of previously released testcases. We use the benchmark to provide the first experimental comparison of existing algorithms and identify the factors impacting the hardness of verification problems.Comment: Updated version of "Piecewise Linear Neural Network verification: A comparative study

MedleySolver: Online SMT Algorithm Selection

Satisfiability modulo theories (SMT) solvers implement a wide range of optimizations that are often tailored to a particular class of problems, and that differ significantly between solvers. As a result, one solver may solve a query quickly while another might be flummoxed completely. Predicting the performance of a given solver is difficult for users of SMT-driven applications, particularly when the problems they have to solve do not fall neatly into a well-understood category. In this paper, we propose an online algorithm selection framework for SMT called MedleySolver that predicts the relative performances of a set of SMT solvers on a given query, distributes time amongst the solvers, and deploys the solvers in sequence until a solution is obtained. We evaluate MedleySolver against the best available alternative, an offline learning technique, in terms of pure performance and practical usability for a typical SMT user. We find that with no prior training, MedleySolver solves 93.9% of the queries solved by the virtual best solver selector achieving 59.8% of the par-2 score of the most successful individual solver, which solves 87.3%. For comparison, the best available alternative takes longer to train than MedleySolver takes to solve our entire set of 2000 queries