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

Low-rank semidefinite programming for the MAX2SAT problem

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.Comment: Accepted at AAAI'19. The code can be found at https://github.com/locuslab/mixsa

Exploiting Resolution-based Representations for MaxSAT Solving

Most recent MaxSAT algorithms rely on a succession of calls to a SAT solver in order to find an optimal solution. In particular, several algorithms take advantage of the ability of SAT solvers to identify unsatisfiable subformulas. Usually, these MaxSAT algorithms perform better when small unsatisfiable subformulas are found early. However, this is not the case in many problem instances, since the whole formula is given to the SAT solver in each call. In this paper, we propose to partition the MaxSAT formula using a resolution-based graph representation. Partitions are then iteratively joined by using a proximity measure extracted from the graph representation of the formula. The algorithm ends when only one partition remains and the optimal solution is found. Experimental results show that this new approach further enhances a state of the art MaxSAT solver to optimally solve a larger set of industrial problem instances

Incremental bounded model checking for embedded software

Program analysis is on the brink of mainstream usage in embedded systems development. Formal verification of behavioural requirements, finding runtime errors and test case generation are some of the most common applications of automated verification tools based on bounded model checking (BMC). Existing industrial tools for embedded software use an off-the-shelf bounded model checker and apply it iteratively to verify the program with an increasing number of unwindings. This approach unnecessarily wastes time repeating work that has already been done and fails to exploit the power of incremental SAT solving. This article reports on the extension of the software model checker CBMC to support incremental BMC and its successful integration with the industrial embedded software verification tool BTC EMBEDDED TESTER. We present an extensive evaluation over large industrial embedded programs, mainly from the automotive industry. We show that incremental BMC cuts runtimes by one order of magnitude in comparison to the standard non-incremental approach, enabling the application of formal verification to large and complex embedded software. We furthermore report promising results on analysing programs with arbitrary loop structure using incremental BMC, demonstrating its applicability and potential to verify general software beyond the embedded domain

Relaxation and Metastability in the RandomWalkSAT search procedure

An analysis of the average properties of a local search resolution procedure for the satisfaction of random Boolean constraints is presented. Depending on the ratio alpha of constraints per variable, resolution takes a time T_res growing linearly (T_res \sim tau(alpha) N, alpha < alpha_d) or exponentially (T_res \sim exp(N zeta(alpha)), alpha > alpha_d) with the size N of the instance. The relaxation time tau(alpha) in the linear phase is calculated through a systematic expansion scheme based on a quantum formulation of the evolution operator. For alpha > alpha_d, the system is trapped in some metastable state, and resolution occurs from escape from this state through crossing of a large barrier. An annealed calculation of the height zeta(alpha) of this barrier is proposed. The polynomial/exponentiel cross-over alpha_d is not related to the onset of clustering among solutions.Comment: 23 pages, 11 figures. A mistake in sec. IV.B has been correcte