Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

Automated Fixing of Programs with Contracts

This paper describes AutoFix, an automatic debugging technique that can fix faults in general-purpose software. To provide high-quality fix suggestions and to enable automation of the whole debugging process, AutoFix relies on the presence of simple specification elements in the form of contracts (such as pre- and postconditions). Using contracts enhances the precision of dynamic analysis techniques for fault detection and localization, and for validating fixes. The only required user input to the AutoFix supporting tool is then a faulty program annotated with contracts; the tool produces a collection of validated fixes for the fault ranked according to an estimate of their suitability. In an extensive experimental evaluation, we applied AutoFix to over 200 faults in four code bases of different maturity and quality (of implementation and of contracts). AutoFix successfully fixed 42% of the faults, producing, in the majority of cases, corrections of quality comparable to those competent programmers would write; the used computational resources were modest, with an average time per fix below 20 minutes on commodity hardware. These figures compare favorably to the state of the art in automated program fixing, and demonstrate that the AutoFix approach is successfully applicable to reduce the debugging burden in real-world scenarios.Comment: Minor changes after proofreadin

Automating Program Verification and Repair Using Invariant Analysis and Test Input Generation

Software bugs are a persistent feature of daily life---crashing web browsers, allowing cyberattacks, and distorting the results of scientific computations. One approach to improving software uses program invariants---mathematical descriptions of program behaviors---to verify code and detect bugs. Current invariant generation techniques lack support for complex yet important forms of invariants, such as general polynomial relations and properties of arrays. As a result, we lack the ability to conduct precise analysis of programs that use this common data structure. This dissertation presents DIG, a static and dynamic analysis framework for discovering several useful classes of program invariants, including (i) nonlinear polynomial relations, which are fundamental to many scientific applications; disjunctive invariants, (ii) which express branching behaviors in programs; and (iii) properties about multidimensional arrays, which appear in many practical applications. We describe theoretical and empirical results showing that DIG can efficiently and accurately find many important invariants in real-world uses, e.g., polynomial properties in numerical algorithms and array relations in a full AES encryption implementation. Automatic program verification and synthesis are long-standing problems in computer science. However, there has been a lot of work on program verification and less so on program synthesis. Consequently, important synthesis tasks, e.g., generating program repairs, remain difficult and time-consuming. This dissertation proves that certain formulations of verification and synthesis are equivalent, allowing for direct applications of techniques and tools between these two research areas. Based on these ideas, we develop CETI, a tool that leverages existing verification techniques and tools for automatic program repair. Experimental results show that CETI can have higher success rates than many other standard program repair methods

Code-based Automated Program Fixing

Many programmers, when they encounter an error, would like to have the benefit of automatic fix suggestions---as long as they are, most of the time, adequate. Initial research in this direction has generally limited itself to specific areas, such as data structure classes with carefully designed interfaces, and relied on simple approaches. To provide high-quality fix suggestions in a broad area of applicability, the present work relies on the presence of contracts in the code, and on the availability of dynamic analysis to gather evidence on the values taken by expressions derived from the program text. The ideas have been built into the AutoFix-E2 automatic fix generator. Applications of AutoFix-E2 to general-purpose software, such as a library to manipulate documents, show that the approach provides an improvement over previous techniques, in particular purely model-based approaches