Article

# Branching bisimulation for probabilistic systems: Characteristics and decidability.

Theoretical Computer Science (Impact Factor: 0.49). 01/2006; 356:325-355. DOI: 10.1016/j.tcs.2006.02.010

Source: DBLP

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**ABSTRACT:**To assess the definitions for "poor ovarian responders" used among randomized trials for the treatment of women with impaired response to stimulation. Systematic review. None. Poor ovarian responders. Treatment modalities for the management of poor ovarian responders. Number and nature of the criteria used to define poor ovarian response to stimulation and threshold values used. Among 47 randomized trials, 41 different definitions for the patients with poor ovarian response have been used. No more than 3 trials used the same definition, whereas even trials from the same research groups used different definitions across different trials. None of the criteria used was adopted in more than 50% of the trials. Age and antral follicle count were adopted only in 9% of the definitions, whereas the criteria of number of follicles on the final stimulation day and number of oocytes retrieved were used in more than 40% of the trials; nonetheless, even for these criteria, the threshold values were consistently different. The variability regarding the definition of poor ovarian responders appears to be striking. Although the Bologna criteria developed by European Society for Human Reproduction and Embryology consensus in 2011 aim to define a consistent group of patients, their applicability needs to be tested through clinical trials. Meanwhile, meta-analyses of the currently available trials should be strongly discouraged because they may lead to the adoption of interventions of ambiguous value.Fertility and sterility 11/2011; 96(5):1058-61.e7. · 3.97 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A notion of branching bisimilarity for the alternating model of probabilistic systems, compatible with parallel composition, is defined. For a congruence result, an internal transition immediately followed by a non-trivial probability distribution is not considered inert. A weaker definition of branching bisimilarity for the same model has been given earlier. Here we show that our branching bisimulation is the coarsest congruence for parallel composition that is included in the weaker version. To support the use of the present equivalence as a reduction technique, we also show that probabilistic CTL formulae are preserved by our equivalence, and we provide a polynomial-time algorithm deciding branching bisimilarity.Theor. Comput. Sci. 01/2012; 413:58-72. - [Show abstract] [Hide abstract]

**ABSTRACT:**Labeled transition systems are typically used as behavioral models of concurrent processes. Their labeled transitions define a one-step state-to-state reachability relation. This model can be generalized by modifying the transition relation to associate a state reachability distribution with any pair consisting of a source state and a transition label. The state reachability distribution is a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. They can be defined on ULTraS by relying on appropriate measure functions that express the degree of reachability of a set of states when performing multi-step computations. It is shown that the specializations of bisimulation, trace, and testing equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models except when nondeterminism and probability/stochasticity coexist; then new equivalences pop up.Information and Computation. 04/2013; 225:29–82.

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