A Symbolic Algorithm for Optimal Markov Chain Lumping

Many approaches to tackle the state explosion problem of Markov chains are based on the notion of lumpability, which allows computation of measures using the quotient Markov chain, which, in some cases, has much smaller state space than the original one. We present, for the first time, a symbolic algorithm and its implementation for the lumping of Markov chains that are represented using Multi-Terminal Binary Decision Diagrams. The algorithm is optimal, i.e., generates the smallest possible quotient Markov chain. Our experiments on various configurations of two example models show that the algorithm (1) handles significantly larger state spaces than an explicit algorithm, (2) is in the best case, faster than an efficient explicit algorithm while not prohibitively slower in the worst case, and (3) generates quotient Markov chains that are several orders of magnitude smaller than ones generated by a model-dependent symbolic lumping algorithm.