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We first study labeled transition systems with explicit successfultermination. We establish the notions of strong, weak, and branchingbisimulation in terms of boolean matrix theory, introducing thus a novel andpowerful algebraic apparatus. Next we consider Markov reward chains which arestandardly presented in real matrix theory. By interpreting the obtained matrixconditions for bisimulations in this setting, we automatically obtain thedefinitions of strong, weak, and branching bisimulation for Markov rewardchains. The obtained strong and weak bisimulations are shown to coincide withsome existing notions, while the obtained branching bisimulation is new, butits usefulness is questionable.

Strong, Weak and Branching Bisimulation for Transition Systems and Markov Reward Chains: A Unifying Matrix Approach