We consider reactive probabilistic labelled transition systems (rplts), a model where internal choices are refined by probabilistic choices. In this setting, we study the relationship between linear-time and may-testing semantics, where an angelic view of nondeterminism is taken. Building on the model of d-trees of Cleaveland et al., we first introduce a clean model of probabilistic may-testing, based on simple concepts from measure theory. In particular, we define a probability space where statements of the form "p may pass test o" naturally correspond to measurable events. We then obtain an observer-independent characterization of the may-testing preorder, based on comparing the probability of sets of traces, rather than of individual traces. This entails that may-testing is strictly finer than linear-time semantics. Next, we characterize the may-testing preorder in terms of the probability of satisfying safety properties, expressed as languages of infinite trees rather than traces. We then identify a significative subclass of rplts where linear and may-testing semantics do coincide: these are the separated rplts, where actions are partitioned into probabilistic and nondeterministic ones, and at each state only one type is available. © 2011 IFIP International Federation for Information Processing.
CITATION STYLE
Acciai, L., Boreale, M., & De Nicola, R. (2011). Linear-time and may-testing in a probabilistic reactive setting. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6722 LNCS, pp. 29–43). https://doi.org/10.1007/978-3-642-21461-5_2
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