Three partition refinement algorithms
SIAM Journal on Computing
CCS expressions finite state processes, and three problems of equivalence
Information and Computation
Dynamic congruence vs. progressing bisimulation for CCS
Fundamenta Informaticae - Special issue on mathematical foundations of computer science '91
Branching time and abstraction in bisimulation semantics
Journal of the ACM (JACM)
A compositional approach to performance modelling
A compositional approach to performance modelling
Communication and Concurrency
Performance measure sensitive congruences for Markovian process algebras
Theoretical Computer Science
Weak Bisimulation for Fully Probabilistic Processes
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Lumping Markov Chains with Silent Steps
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
A Process Algebraic Approach to Software Architecture Design
A Process Algebraic Approach to Software Architecture Design
Comparative branching-time semantics for Markov chains
Information and Computation
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The Markovian behavioral equivalences defined so far treat exponentially timed internal actions like any other action. Since an exponentially timed internal action has a nonzero duration, it can be observed whenever it is executed between a pair of exponentially timed noninternal actions. However, no difference may be noted at steady state between a sequence of exponentially timed internal actions and a single exponentially timed internal action as long as their average durations coincide. We show that Milner's construction to derive a weak bisimulation congruence for nondeterministic processes can be extended to sequential Markovian processes in a way that captures the above situation. The resulting weak Markovian bisimulation congruence admits a sound and complete axiomatization, induces an exact CTMC-level aggregation at steady state, and is decidable in polynomial time for finite-state processes having no cycles of exponentially timed internal actions.