Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Symbolic partition refinement with automatic balancing of time and space
Performance Evaluation
Counterexample generation for Markov chains using SMT-based bounded model checking
FMOODS'11/FORTE'11 Proceedings of the joint 13th IFIP WG 6.1 and 30th IFIP WG 6.1 international conference on Formal techniques for distributed systems
PARAM: a model checker for parametric markov models
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Correctness issues of symbolic bisimulation computation for markov chains
MMB&DFT'10 Proceedings of the 15th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
APEX: an analyzer for open probabilistic programs
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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Many approaches to tackle the state-space explosion problem ofMarkov chains are based on the notion of lumpa- bility (a.k.a. probabilistic bisimulation), which allows com- putation of measures using the quotient Markov chain, which, in some cases, has much smaller state space than the original one. We present a new signature-based algorithm for computing the optimal (i.e., smallest possible) quotient Markov chain, prove its correctness, and implement it sym- bolically for Markov chains represented as Multi-Terminal BDDs (MTBDDs). The algorithm is very time-efficient be- cause we translate the core operation of the algorithm, i.e., the computation of the signatures, into symbolic operations. Our experiments on various configurations of three example models with different levels of lumpability show that the al- gorithm (1) handles significantly larger state spaces than an explicit algorithm, (2) outperforms a very efficient explicit algorithm for significantly lumpableMarkov chains while it is not prohibitively slower in the worst case, and (3) out- performs our previous optimal symbolic algorithm [10] in terms of running time although it has higher space require- ment for most of the configurations.