Dynamic Partial Order Reduction Algorithm Research Articles

Truly stateless, optimal dynamic partial order reduction

Dynamic partial order reduction (DPOR) verifies concurrent programs by exploring all their interleavings up to some equivalence relation, such as the Mazurkiewicz trace equivalence. Doing so involves a complex trade-off between space and time. Existing DPOR algorithms are either exploration-optimal (i.e., explore exactly only interleaving per equivalence class) but may use exponential memory in the size of the program, or maintain polynomial memory consumption but potentially explore exponentially many redundant interleavings. In this paper, we show that it is possible to have the best of both worlds: exploring exactly one interleaving per equivalence class with linear memory consumption. Our algorithm, TruSt, formalized in Coq, is applicable not only to sequential consistency, but also to any weak memory model that satisfies a few basic assumptions, including TSO, PSO, and RC11. In addition, TruSt is embarrassingly parallelizable: its different exploration options have no shared state, and can therefore be explored completely in parallel. Consequently, TruSt outperforms the state-of-the-art in terms of memory and/or time.

Data-centric dynamic partial order reduction

We present a new dynamic partial-order reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partial-order reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes ( Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is control-centric, our new definition is data-centric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called data-centric DPOR, based on the observation equivalence. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our data-centric DPOR algorithm remains optimal under this trace equivalence. Finally, we perform a basic experimental comparison between the existing Mazurkiewicz-based DPOR and our data-centric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes.

Source Sets

Stateless model checking is a powerful method for program verification that, however, suffers from an exponential growth in the number of explored executions. A successful technique for reducing this number, while still maintaining complete coverage, is Dynamic Partial Order Reduction (DPOR), an algorithm originally introduced by Flanagan and Godefroid in 2005 and since then not only used as a point of reference but also extended by various researchers. In this article, we present a new DPOR algorithm, which is the first to be provably optimal in that it always explores the minimal number of executions. It is based on a novel class of sets, called source sets , that replace the role of persistent sets in previous algorithms. We begin by showing how to modify the original DPOR algorithm to work with source sets, resulting in an efficient and simple-to-implement algorithm, called source-DPOR . Subsequently, we enhance this algorithm with a novel mechanism, called wakeup trees , that allows the resulting algorithm, called optimal-DPOR , to achieve optimality. Both algorithms are then extended to computational models where processes may disable each other, for example, via locks. Finally, we discuss tradeoffs of the source- and optimal-DPOR algorithm and present programs that illustrate significant time and space performance differences between them. We have implemented both algorithms in a publicly available stateless model checking tool for Erlang programs, while the source-DPOR algorithm is at the core of a publicly available stateless model checking tool for C/pthread programs running on machines with relaxed memory models. Experiments show that source sets significantly increase the performance of stateless model checking compared to using the original DPOR algorithm and that wakeup trees incur only a small overhead in both time and space in practice.

Stateless model checking for TSO and PSO

We present a technique for efficient stateless model checking of programs that execute under the relaxed memory models TSO and PSO. The basis for our technique is a novel representation of executions under TSO and PSO, called chronological traces. Chronological traces induce a partial order relation on relaxed memory executions, capturing dependencies that are needed to represent the interaction via shared variables. They are optimal in the sense that they only distinguish computations that are inequivalent under the widely-used representation by Shasha and Snir. This allows an optimal dynamic partial order reduction algorithm to explore a minimal number of executions while still guaranteeing full coverage. We apply our techniques to check, under the TSO and PSO memory models, LLVM assembly produced for C/pthreads programs. Our experiments show that our technique reduces the verification effort for relaxed memory models to be almost that for the standard model of sequential consistency. This article is an extended version of Abdulla et al. (Tools and algorithms for the construction and analysis of systems, Springer, New York, pp 353–367, 2015), appearing in TACAS 2015.

Optimal dynamic partial order reduction

Stateless model checking is a powerful technique for program verification, which however suffers from an exponential growth in the number of explored executions. A successful technique for reducing this number, while still maintaining complete coverage, is Dynamic Partial Order Reduction (DPOR). We present a new DPOR algorithm, which is the first to be provably optimal in that it always explores the minimal number of executions. It is based on a novel class of sets, called source sets , which replace the role of persistent sets in previous algorithms. First, we show how to modify an existing DPOR algorithm to work with source sets, resulting in an efficient and simple to implement algorithm. Second, we extend this algorithm with a novel mechanism, called wakeup trees , that allows to achieve optimality. We have implemented both algorithms in a stateless model checking tool for Erlang programs. Experiments show that source sets significantly increase the performance and that wakeup trees incur only a small overhead in both time and space.