Rupak Majumdar

Lazy abstraction

One approach to model checking software is based on the abstract-check-refine paradigm: build an abstract model, then check the desired property, and if the check fails, refine the model and start over. We introduce the concept of lazy abstraction to integrate and optimize the three phases of the abstract-check-refine loop. Lazy abstraction continuously builds and refines a single abstract model on demand, driven by the model checker, so that different parts of the model may exhibit different degrees of precision, namely just enough to verify the desired property. We present an algorithm for model checking safety properties using lazy abstraction and describe an implementation of the algorithm applied to C programs. We also provide sufficient conditions for the termination of the method.

Automatic predicate abstraction of C programs

Model checking has been widely successful in validating and debugging designs in the hardware and protocol domains. However, state-space explosion limits the applicability of model checking tools, so model checkers typically operate on abstractions of systems. Recently, there has been significant interest in applying model checking to software. For infinite-state systems like software, abstraction is even more critical. Techniques for abstracting software are a prerequisite to making software model checking a reality. We present the first algorithm to automatically construct a predicate abstraction of programs written in am industrial programming language such as C, and its implementation in a tool -- C2BP. The C2BP tool is part of the SLAM toolkit, which uses a combination of predicate abstraction, model checking, symbolic reasoning, and iterative refinement to statically check temporal safety properties of programs. Predicate abstraction of software has many applications, including detecting program errors, synthesizing program invariants, and improving the precision of program analyses through predicate sensitivity. We discuss our experience applying the C2BP predicate abstraction tool to a variety of problems, ranging from checking that list-manipulating code preserves heap invariants to finding errors in Windows NT device drivers.

The software model checker BLAST Applications to software engineering

Blast is an automatic verification tool for checking temporal safety properties of C programs. Given a C program and a temporal safety property, Blast either statically proves that the program satisfies the safety property, or provides an execution path that exhibits a violation of the property (or, since the problem is undecidable, does not terminate). Blast constructs, explores, and refines abstractions of the program state space based on lazy predicate abstraction and interpolation-based predicate discovery. This paper gives an introduction to Blast and demonstrates, through two case studies, how it can be applied to program verification and test-case generation. In the first case study, we use Blast to statically prove memory safety for C programs. We use CCured, a type-based memory-safety analyzer, to annotate a program with run-time assertions that check for safe memory operations. Then, we use Blast to remove as many of the run-time checks as possible (by proving that these checks never fail), and to generate execution scenarios that violate the assertions for the remaining run-time checks. In our second case study, we use Blast to automatically generate test suites that guarantee full coverage with respect to a given predicate. Given a C program and a target predicate p, Blast determines the program locations q for which there exists a program execution that reaches q with p true, and automatically generates a set of test vectors that cause such executions. Our experiments show that Blast can provide automated, precise, and scalable analysis for C programs.

Abstractions from proofs

The success of model checking for large programs depends crucially on the ability to efficiently construct parsimonious abstractions. A predicate abstraction is parsimonious if at each control location, it specifies only relationships between current values of variables, and only those which are required for proving correctness. Previous methods for automatically refining predicate abstractions until sufficient precision is obtained do not systematically construct parsimonious abstractions: predicates usually contain symbolic variables, and are added heuristically and often uniformly to many or all control locations at once. We use Craig interpolation to efficiently construct, from a given abstract error trace which cannot be concretized, a parsominous abstraction that removes the trace. At each location of the trace, we infer the relevant predicates as an interpolant between the two formulas that define the past and the future segment of the trace. Each interpolant is a relationship between current values of program variables, and is relevant only at that particular program location. It can be found by a linear scan of the proof of infeasibility of the trace.We develop our method for programs with arithmetic and pointer expressions, and call-by-value function calls. For function calls, Craig interpolation offers a systematic way of generating relevant predicates that contain only the local variables of the function and the values of the formal parameters when the function was called. We have extended our model checker BLAST with predicate discovery by Craig interpolation, and applied it successfully to C programs with more than 130,000 lines of code, which was not possible with approaches that build less parsimonious abstractions.

Software verification with BLAST

Blast (the Berkeley Lazy Abstraction Software verification Tool) is a verification system for checking safety properties of C programs using automatic property-driven construction and model checking of software abstractions. Blast implements an abstract-model check-refine loop to check for reachability of a specified label in the program. The abstract model is built on the fly using predicate abstraction. This model is then checked for reachability. If there is no (abstract) path to the specified error label, Blast reports that the system is safe and produces a succinct proof. Otherwise, it checks if the path is feasible using symbolic execution of the program. If the path is feasible, Blast outputs the path as an error trace, otherwise, it uses the infeasibility of the path to refine the abstract model. Blast short-circuits the loop from abstraction to verification to refinement, integrating the three steps tightly through “lazy abstraction” [5]. This integration can offer significant advantages in performance by avoiding the repetition of work from one iteration of the loop to the next.

The software model checker B last : Applications to software engineering

Blast is an automatic verification tool for checking temporal safety properties of C programs. Given a C program and a temporal safety property, Blast either statically proves that the program satisfies the safety property, or provides an execution path that exhibits a violation of the property (or, since the problem is undecidable, does not terminate). Blast constructs, explores, and refines abstractions of the program state space based on lazy predicate abstraction and interpolation-based predicate discovery. This paper gives an introduction to Blast and demonstrates, through two case studies, how it can be applied to program verification and test-case generation. In the first case study, we use Blast to statically prove memory safety for C programs. We use CCured, a type-based memory-safety analyzer, to annotate a program with run-time assertions that check for safe memory operations. Then, we use Blast to remove as many of the run-time checks as possible (by proving that these checks never fail), and to generate execution scenarios that violate the assertions for the remaining run-time checks. In our second case study, we use Blast to automatically generate test suites that guarantee full coverage with respect to a given predicate. Given a C program and a target predicate p, Blast determines the program locations q for which there exists a program execution that reaches q with p true, and automatically generates a set of test vectors that cause such executions. Our experiments show that Blast can provide automated, precise, and scalable analysis for C programs.

Hybrid Concolic Testing

We present hybrid concolic testing, an algorithm that interleaves random testing with concolic execution to obtain both a deep and a wide exploration of program state space. Our algorithm generates test inputs automatically by interleaving random testing until saturation with bounded exhaustive symbolic exploration of program points. It thus combines the ability of random search to reach deep program states quickly together with the ability of concolic testing to explore states in a neighborhood exhaustively. We have implemented our algorithm on top of CUTE and applied it to obtain better branch coverage for an editor implementation (VIM 5.7, 150 K lines of code) as well as a data structure implementation in C. Our experiments suggest that hybrid concolic testing can handle large programs and provide, for the same testing budget, almost 4times the branch coverage than random testing and almost 2times that of concolic testing.

Software model checking

We survey recent progress in software model checking.

Generating tests from counterexamples

We have extended the software model checker BLAST to automatically generate test suites that guarantee full coverage with respect to a given predicate. More precisely, given a C program and a target predicate p, BLAST determines the set L of program locations which program execution can reach with p true, and automatically generates a set of test vectors that exhibit the truth of p at all locations in L. We have used BLAST to generate test suites and to detect dead code in C programs with up to 30 K lines of code. The analysis and test vector generation is fully automatic (no user intervention) and exact (no false positives).

Dynamic test input generation for database applications

We describe an algorithm for automatic test input generation for database applications. Given a program in an imperative language that interacts with a database through API calls, our algorithm generates both input data for the program as well as suitable database records to systematically explore all paths of the program, including those paths whose execution depend on data returned by database queries. Our algorithm is based on concolic execution, where the program is run with concrete inputs and simultaneously also with symbolic inputs for both program variables as well as the database state. The symbolic constraints generated along a path enable us to derive new input values and new database records that can cause execution to hit uncovered paths. Simultaneously, the concrete execution helps to retain precision in the symbolic computations by allowing dynamic values to be used in the symbolic executor. This allows our algorithm, for example, to identify concrete SQL queries made by the program, even if these queries are built dynamically. The contributions of this paper are the following. We develop an algorithm that can track symbolic constraints across language boundaries and use those constraints in conjunction with a novel constraint solver to generate both program inputs and database state. We propose a constraint solver that can solve symbolic constraints consisting of both linear arithmetic constraints over variables as well as string constraints (string equality, disequality, as well as membership in regular languages). Finally, we provide an evaluation of the algorithm on a Java implementation of MediaWiki, a popular wiki package that interacts with a database back-end.