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Linear-Time and May-Testing in a Probabilistic Reactive Setting

Acciai, Lucia and Boreale, Michele and De Nicola, Rocco Linear-Time and May-Testing in a Probabilistic Reactive Setting. In: Formal Techniques for Distributed Systems (FMOODS/FORTE 2011). Lecture Notes in Computer Science, 6722 . Springer, pp. 29-43. (2011)

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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.

Item Type: Book Section
Identification Number: 10.1007/978-3-642-21461-5_2
Additional Information: © IFIP International Federation for Information Processing 2011
Uncontrolled Keywords: probabilistic transition systems – linear time – testing equivalence – safety
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Rocco De Nicola
Date Deposited: 16 Jun 2011 09:04
Last Modified: 11 Jul 2011 14:36
URI: http://eprints.imtlucca.it/id/eprint/420

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