Theory of linear and integer programming
Theory of linear and integer programming
Bisimulation through probabilistic testing
Information and Computation
A polynomial-time algorithm for the equivalence of probabilistic automata
SIAM Journal on Computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
On path equivalence of nondeterministic finite automata
Information Processing Letters
A compositional approach to performance modelling
A compositional approach to performance modelling
Communication and Concurrency
The consensus string problem and the complexity of comparing hidden Markov models
Journal of Computer and System Sciences - Computational biology 2002
Polynomial Time Algorithms for Testing Probabilistic Bisimulation and Simulation
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Optimal state-space lumping in Markov chains
Information Processing Letters
On the Hardness of Graph Isomorphism
SIAM Journal on Computing
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
Approximating and computing behavioural distances in probabilistic transition systems
Theoretical Computer Science
Recursively defined metric spaces without contraction
Theoretical Computer Science
ISPEC '09 Proceedings of the 5th International Conference on Information Security Practice and Experience
Labelled Markov Processes
Bisimulation minimisation mostly speeds up probabilistic model checking
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
On the Complexity of Nash Equilibria and Other Fixed Points
SIAM Journal on Computing
Simple O(m log n) time Markov chain lumping
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Computing game metrics on markov decision processes
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Coalgebraic trace semantics for probabilistic transition systems based on measure theory
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
BPA bisimilarity is EXPTIME-hard
Information Processing Letters
On-the-Fly exact computation of bisimilarity distances
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
The bisimdist library: efficient computation of bisimilarity distances for markovian models
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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Probabilistic bisimilarity is a fundamental notion of equivalence on labelled Markov chains. It has a natural generalisation to a probabilistic bisimilarity pseudometric, whose definition involves the Kantorovich metric on probability distributions. The pseudometric has discounted and undiscounted variants, according to whether one discounts the future in observing discrepancies between states. This paper is concerned with the complexity of computing probabilistic bisimilarity and the probabilistic bisimilarity pseudometric on labelled Markov chains. We show that the problem of computing probabilistic bisimilarity is P-hard by reduction from the monotone circuit value problem. We also show that the discounted pseudometric is rational and can be computed exactly in polynomial time using the network simplex algorithm and the continued fraction algorithm. In the undiscounted case we show that the pseudometric is again rational and can be computed exactly in polynomial time using the ellipsoid algorithm. Finally, using the notion of couplings on Markov chains, we show that the pseudometric can be used to compute bounds on the variational distance of trace distributions, which is NP-hard to compute directly.