Distributed and structured analysis approaches to study large and complex systems
Lectures on formal methods and performance analysis
Out-of-Core Solution of Large Linear Systems of Equations Arising from Stochastic Modelling
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
PRISM: Probabilistic Symbolic Model Checker
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
State Space Construction and Steady--State Solution of GSPNs on a Shared--Memory Multiprocessor
PNPM '97 Proceedings of the 6th International Workshop on Petri Nets and Performance Models
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Automatic performance tuning of sparse matrix kernels
Automatic performance tuning of sparse matrix kernels
Distributed disk-based algorithms for model checking very large Markov chains
Formal Methods in System Design
The Design of a Multicore Extension of the SPIN Model Checker
IEEE Transactions on Software Engineering
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Efficient Probabilistic Model Checking on General Purpose Graphics Processors
Proceedings of the 16th International SPIN Workshop on Model Checking Software
Implementing sparse matrix-vector multiplication on throughput-oriented processors
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
CUDA Accelerated LTL Model Checking
ICPADS '09 Proceedings of the 2009 15th International Conference on Parallel and Distributed Systems
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Parallel probabilistic model checking on general purpose graphics processors
International Journal on Software Tools for Technology Transfer (STTT) - SPIN 2009
GPU-PRISM: An Extension of PRISM for General Purpose Graphics Processing Units
PDMC-HIBI '10 Proceedings of the 2010 Ninth International Workshop on Parallel and Distributed Methods in Verification, and Second International Workshop on High Performance Computational Systems Biology
Incremental quantitative verification for Markov decision processes
DSN '11 Proceedings of the 2011 IEEE/IFIP 41st International Conference on Dependable Systems&Networks
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We present several methods to improve the run times of probabilistic model checking on general-purpose graphics processing units (GPUs). The methods enhance sparse matrix-vector multiplications, which are in the core of the probabilistic model checking algorithms. The improvement is based on the analysis of the transition matrix structures corresponding to state spaces of a selection of examples from the literature. Our first method defines an enumeration of the matrix elements (states of the Markov chains), based on breadth-first search which can lead to a more regular representation of the matrices. We introduce two additional methods that adjust the execution paths and memory access patterns of the individual processors of the GPU. They exploit the specific features of the transition matrices arising from probabilistic/stochastic models as well as the logical and physical architectures of the device. We implement the matrix reindexing and the efficient memory access methods in GPU-PRISM, an extension of the probabilistic model checker PRISM. The experiments with the prototype implementation show that each of the methods can bring a significant run time improvement - more than four times compared to the previous version of GPU-PRISM. Moreover, in some cases, the methods are orthogonal and can be used in combination to achieve even greater speed ups.