XSpeed: Accelerating Reachability Analysis on Multi-core Processors

  • Rajarshi RayEmail author
  • Amit Gurung
  • Binayak Das
  • Ezio Bartocci
  • Sergiy Bogomolov
  • Radu Grosu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9434)


We present XSpeed a parallel state-space exploration algorithm for continuous systems with linear dynamics and nondeterministic inputs. The motivation of having parallel algorithms is to exploit the computational power of multi-core processors to speed-up performance. The parallelization is achieved on two fronts. First, we propose a parallel implementation of the support function algorithm by sampling functions in parallel. Second, we propose a parallel state-space exploration by slicing the time horizon and computing the reachable states in the time slices in parallel. The second method can be however applied only to a class of linear systems with invertible dynamics and fixed input. A GP-GPU implementation is also presented following a lazy evaluation strategy on support functions. The parallel algorithms are implemented in the tool XSpeed. We evaluated the performance on two benchmarks including an 28 dimension Helicopter model. Comparison with the sequential counterpart shows a maximum speed-up of almost 7\(\times \) on a 6 core, 12 thread Intel Xeon CPU E5-2420 processor. Our GP-GPU implementation shows a maximum speed-up of 12\(\times \) over the sequential implementation and 53\(\times \) over SpaceEx (LGG scenario), the state of the art tool for reachability analysis of linear hybrid systems. Experiments illustrate that our parallel algorithm with time slicing not only speeds-up performance but also improves precision.


Support Function Global Memory Reachable State Thread Block Reachability Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported in part by the European Research Council (ERC) under grant 267989 (QUAREM) and by the Austrian Science Fund (FWF) under grants S11402-N23, S11405-N23 and S11412-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Rajarshi Ray
    • 1
    Email author
  • Amit Gurung
    • 1
  • Binayak Das
    • 1
  • Ezio Bartocci
    • 2
  • Sergiy Bogomolov
    • 3
  • Radu Grosu
    • 2
  1. 1.National Institute of Technology MeghalayaShillongIndia
  2. 2.Vienna University of TechnologyViennaAustria
  3. 3.Institute of Science and Technology AustriaKlosterneuburgAustria

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