Lazy Parallel Kronecker Algebra-Operations on Heterogeneous Multicores

  • Wasuwee Sodsong
  • Robert Mittermayr
  • Yoojin Park
  • Bernd Burgstaller
  • Johann Blieberger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10417)


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\(\times \) 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.


Kronecker algebra Lazy evaluation Deadlock detection Heterogeneous multicores GPUs 



This research was supported by the Austrian Science Fund (FWF) project I 1035N23, and by the Next-Generation Information Computing Development Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT & Future Planning under grant NRF2015M3C4A7065522.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Yonsei UniversitySeoulKorea
  2. 2.Vienna University of TechnologyViennaAustria

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