Software Model Checking with Explicit Scheduler and Symbolic Threads

In many practical application domains, the software is organized into a set of threads, whose activation is exclusive and controlled by a cooperative scheduling policy: threads execute, without any interruption, until they either terminate or yield the control explicitly to the scheduler. The formal verification of such software poses significant challenges. On the one side, each thread may have infinite state space, and might call for abstraction. On the other side, the scheduling policy is often important for correctness, and an approach based on abstracting the scheduler may result in loss of precision and false positives. Unfortunately, the translation of the problem into a purely sequential software model checking problem turns out to be highly inefficient for the available technologies. We propose a software model checking technique that exploits the intrinsic structure of these programs. Each thread is translated into a separate sequential program and explored symbolically with lazy abstraction, while the overall verification is orchestrated by the direct execution of the scheduler. The approach is optimized by filtering the exploration of the scheduler with the integration of partial-order reduction. The technique, called ESST (Explicit Scheduler, Symbolic Threads) has been implemented and experimentally evaluated on a significant set of benchmarks. The results demonstrate that ESST technique is way more effective than software model checking applied to the sequentialized programs, and that partial-order reduction can lead to further performance improvements.Comment: 40 pages, 10 figures, accepted for publication in journal of logical methods in computer scienc

Predicate Abstraction with Indexed Predicates

Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking. We consider models containing first-order state variables, where the system state includes mutable functions and predicates. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified variables to describe invariant properties of the first-order state variables. We provide a formal justification of the soundness of our approach and describe how it has been used to verify several hardware and software designs, including a directory-based cache coherence protocol.Comment: 27 pages, 4 figures, 1 table, short version appeared in International Conference on Verification, Model Checking and Abstract Interpretation (VMCAI'04), LNCS 2937, pages = 267--28

Sequentializing Parameterized Programs

We exhibit assertion-preserving (reachability preserving) transformations from parameterized concurrent shared-memory programs, under a k-round scheduling of processes, to sequential programs. The salient feature of the sequential program is that it tracks the local variables of only one thread at any point, and uses only O(k) copies of shared variables (it does not use extra counters, not even one counter to keep track of the number of threads). Sequentialization is achieved using the concept of a linear interface that captures the effect an unbounded block of processes have on the shared state in a k-round schedule. Our transformation utilizes linear interfaces to sequentialize the program, and to ensure the sequential program explores only reachable states and preserves local invariants.Comment: In Proceedings FIT 2012, arXiv:1207.348

Context-aware counter abstraction

The trend towards multi-core computing has made concurrent software an important target of computer-aided verification. Unfortunately, Model Checkers for such software suffer tremendously from combinatorial state space explosion. We show how to apply counter abstraction to real-world concurrent programs to factor out redundancy due to thread replication. The traditional global state representation as a vector of local states is replaced by a vector of thread counters, one per local state. In practice, straightforward implementations of this idea are unfavorably sensitive to the number of local states. We present a novel symbolic exploration algorithm that avoids this problem by carefully scheduling which counters to track at any moment during the search. We have carried out experiments on Boolean programs, an abstraction promoted by the success of the Slam project. The experiments give evidence of the applicability of our method to realistic programs, and of the often huge savings obtained in comparison to plain symbolic state space exploration, and to exploration optimized by partial-order methods. To our knowledge, our tool marks the first implementation of counter abstraction to programs with non-trivial local state spaces, resulting in a Model Checker for concurrent Boolean programs that promises true scalabilit

Safety Verification of Phaser Programs

We address the problem of statically checking control state reachability (as in possibility of assertion violations, race conditions or runtime errors) and plain reachability (as in deadlock-freedom) of phaser programs. Phasers are a modern non-trivial synchronization construct that supports dynamic parallelism with runtime registration and deregistration of spawned tasks. They allow for collective and point-to-point synchronizations. For instance, phasers can enforce barriers or producer-consumer synchronization schemes among all or subsets of the running tasks. Implementations %of these recent and dynamic synchronization are found in modern languages such as X10 or Habanero Java. Phasers essentially associate phases to individual tasks and use their runtime values to restrict possible concurrent executions. Unbounded phases may result in infinite transition systems even in the case of programs only creating finite numbers of tasks and phasers. We introduce an exact gap-order based procedure that always terminates when checking control reachability for programs generating bounded numbers of coexisting tasks and phasers. We also show verifying plain reachability is undecidable even for programs generating few tasks and phasers. We then explain how to turn our procedure into a sound analysis for checking plain reachability (including deadlock freedom). We report on preliminary experiments with our open source tool