Lazy Parallel Kronecker Algebra-Operations on Heterogeneous Multicores

Abstract

Kronecker algebra is a matrix calculus which allows the generation of thread interleavings from the source-code of a program. Thread interleavings have been shown effective for proving the absence of deadlocks. Because the number of interleavings grows exponentially in the number of threads, deadlock analysis is still a challenging problem. To make the computation of thread interleavings tractable, we propose a lazy, parallel evaluation method for Kronecker algebra. Our method incorporates the constraints induced by synchronization constructs. To reduce problem size, only interleavings legal under the locking behavior of a program are considered. We leverage the data-parallelism of Kronecker sum- and product-operations for multicores and GPUs. Proposed algebraic transformations further improve performance. For one synthetic and two real-world benchmarks, our GPU implementation is up to 5453× faster than our multi-threaded version. Lazy evaluation significantly reduces memory consumption compared to both the sequential and the multicore versions of the SPIN model-checker.