Reduced Cost Fixing for Maximum Satisfiability

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Survey-propagation decimation through distributed local computations

We discuss the implementation of two distributed solvers of the random K-SAT problem, based on some development of the recently introduced survey-propagation (SP) algorithm. The first solver, called the "SP diffusion algorithm", diffuses as dynamical information the maximum bias over the system, so that variable nodes can decide to freeze in a self-organized way, each variable making its decision on the basis of purely local information. The second solver, called the "SP reinforcement algorithm", makes use of time-dependent external forcing messages on each variable, which let the variables get completely polarized in the direction of a solution at the end of a single convergence. Both methods allow us to find a solution of the random 3-SAT problem in a range of parameters comparable with the best previously described serialized solvers. The simulated time of convergence towards a solution (if these solvers were implemented on a distributed device) grows as log(N).Comment: 18 pages, 10 figure

Cause Clue Clauses: Error Localization using Maximum Satisfiability

Much effort is spent everyday by programmers in trying to reduce long, failing execution traces to the cause of the error. We present a new algorithm for error cause localization based on a reduction to the maximal satisfiability problem (MAX-SAT), which asks what is the maximum number of clauses of a Boolean formula that can be simultaneously satisfied by an assignment. At an intuitive level, our algorithm takes as input a program and a failing test, and comprises the following three steps. First, using symbolic execution, we encode a trace of a program as a Boolean trace formula which is satisfiable iff the trace is feasible. Second, for a failing program execution (e.g., one that violates an assertion or a post-condition), we construct an unsatisfiable formula by taking the trace formula and additionally asserting that the input is the failing test and that the assertion condition does hold at the end. Third, using MAX-SAT, we find a maximal set of clauses in this formula that can be satisfied together, and output the complement set as a potential cause of the error. We have implemented our algorithm in a tool called bug-assist for C programs. We demonstrate the surprising effectiveness of the tool on a set of benchmark examples with injected faults, and show that in most cases, bug-assist can quickly and precisely isolate the exact few lines of code whose change eliminates the error. We also demonstrate how our algorithm can be modified to automatically suggest fixes for common classes of errors such as off-by-one.Comment: The pre-alpha version of the tool can be downloaded from http://bugassist.mpi-sws.or

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

A hybrid constraint programming and semidefinite programming approach for the stable set problem

This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable domain values, based on the solution of a semidefinite relaxation. Using this ranking, we generate the most promising subproblems first, by exploring a search tree using a limited discrepancy strategy. Then the subproblems are being solved using a constraint programming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure. Computational results show that the semidefinite relaxation is very informative, since solutions of good quality are found in the first subproblems, or optimality is proven immediately.Comment: 14 page

Reduced Cost Fixing in MaxSAT

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