Equivalence of labeled Markov chains

We consider the equivalence problem for labeled Markov chains (LMCs), where each state is labeled with an observation. Two LMCs are equivalent if every finite sequence of observations has the same probability of occurrence in the two LMCs. We show that equivalence can be decided in polynomial time, using a reduction to the equivalence problem for probabilistic automata, which is known to be solvable in polynomial time. We provide an alternative algorithm to solve the equivalence problem, which is based on a new definition of bisimulation for probabilistic automata. We also extend the technique to decide the equivalence of weighted probabilistic automata.

Published in:
International Journal Of Foundations Of Computer Science, 19, 549-563
Presented at:
11th International Conference on Developments in Language Theory, Turku, FINLAND, Jul 03-06, 2007

 Record created 2010-11-30, last modified 2018-03-17

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