Accelerating SpMV Multiplication in Probabilistic Model Checkers Using GPUs

• Published in: Theoretical Aspects of Computing - ICTAC 2021 Vol. 12819; pp. 86 - 104
• Main Authors: Khan, Muhammad Hannan, Hassan, Osman, Khan, Shahid
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: GPU; Probabilistic model checking; Sparse matrix-vector multiplication
• ISBN: 3030853144; 9783030853143
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-85315-0_6

Probabilistic model checking is a prominent formal verification technique for analyzing stochastic systems. Probabilistic model checkers hinge upon the sparse matrix-vector (SpMV) multiplications to compute reachability probabilities, i.e., the probability of reaching a target state from a given initial state. Being compute- and memory-intensive task, SpMV is a bottleneck in using probabilistic model checking for analyzing scalable real-world case studies. This paper presents a methodology to accelerate SpMV multiplication in probabilistic model checkers using graphic processing units (GPUs). Since GPUs efficiently execute basic linear algebraic operations such as multiplication, one achieves improvements in computation times. These improvements, however, are not significant in the presence of memory transfer overheads. We apply traditional optimization techniques and hide the memory transfers from the host computer to the GPU inside the state-space-exploration stage. This hiding significantly reduces the latency caused by memory transfers during execution. We implemented the proposed acceleration approach with CUDA-based cuSPARSE API and asynchronous multiple copy algorithms in the probabilistic model checker Storm, with a focus on its SpMV multiplier. In our experiments, we observed 16 times speed up on average over the state-of-the-art.