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

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

Source coding by efficient selection of ground states clusters

In this letter, we show how the Survey Propagation algorithm can be generalized to include external forcing messages, and used to address selectively an exponential number of glassy ground states. These capabilities can be used to explore efficiently the space of solutions of random NP-complete constraint satisfaction problems, providing a direct experimental evidence of replica symmetry breaking in large-size instances. Finally, a new lossy data compression protocol is introduced, exploiting as a computational resource the clustered nature of the space of addressable states.Comment: 4 pages, 4 figure

Systematic techniques for more effective fault localization and program repair

Debugging faulty code is a tedious process that is often quite expensive and can require much manual effort. Developers typically perform debugging in two key steps: (1) fault localization, i.e., identifying the location of faulty line(s) of code; and (2) program repair, i.e., modifying the code to remove the fault(s). Automating debugging to reduce its cost has been the focus of a number of research projects during the last decade, which have introduced a variety of techniques. However, existing techniques suffer from two basic limitations. One, they lack accuracy to handle real programs. Two, they focus on automating only one of the two key steps, thereby leaving the other key step to the developer. Our thesis is that an approach that integrates systematic search based on state-of-the-art constraint solvers with techniques to analyze artifacts that describe application specific properties and behaviors, provides the basis for developing more effective debugging techniques. We focus on faults in programs that operate on structurally complex inputs, such as heap-allocated data or relational databases. Our approach lays the foundation for a unified framework for localization and repair of faults in programs. We embody our thesis in a suite of integrated techniques based on propositional satisfiability solving, correctness specifications analysis, test-spectra analysis, and rule-learning algorithms from machine learning, implement them as a prototype tool-set, and evaluate them using several subject programs.Electrical and Computer Engineerin