Bisimulation through probabilistic testing
Information and Computation
The Metric Analogue of Weak Bisimulation for Probabilistic Processes
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Metrics for Labeled Markov Systems
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
An Algorithm for Quantitative Verification of Probabilistic Transition Systems
CONCUR '01 Proceedings of the 12th International Conference on Concurrency Theory
Probabilistic Simulations for Probabilistic Processes
CONCUR '94 Proceedings of the Concurrency Theory
Metrics for Action-labelled Quantitative Transition Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
| Hi-index | 0.89 |
A behavioural pseudometric is often defined as the least fixed point of a monotone function F on a complete lattice of 1-bounded pseudometrics. According to Tarski@?s fixed point theorem, this least fixed point can be obtained by (possibly transfinite) iteration of F, starting from the least element @? of the lattice. The smallest ordinal @a such that F^@a(@?)=F^@a^+^1(@?) is known as the closure ordinal of F. We prove that if F is also continuous with respect to the sup-norm, then its closure ordinal is @w. We also show that our result gives rise to simpler and modular proofs that the closure ordinal is @w.