Trace and Testing Metrics on Nondeterministic Probabilistic Processes

Abstract

The combination of nondeterminism and probability in concurrent systems lead to the development of several interpretations of process behavior. If we restrict our attention to linear properties only, we can identify three main approaches to trace and testing semantics: the trace distributions, the trace-by-trace and the extremal probabilities approaches. In this paper, we propose novel notions of behavioral metrics that are based on the three classic approaches above, and that can be used to measure the disparities in the linear behavior of processes wrt. trace and testing semantics. We study the properties of these metrics, like non-expansiveness, and we compare their expressive powers. • •

The Theory of Traces for Systems with Nondeterminism and Probability

“…For all x ∈ X and w ∈ A * , it holds that Theorem 23 and Corollary 24 provide a characterisation of ≡, ≡ B and ≡ T in terms of resolutions. We next show that ≡ B coincides with the randomized ⊔-trace equivalence investigated in [40] and inspired by [25], [26].…”

“…It is important to remark here that our resolutions differ from those previously proposed in the literature in the fact that they are reactive rather than fully probabilistic. We observe that however this difference does not affect the greatest probability, and we can therefore show that the may-trace coincides with the randomized ⊔-trace equivalence in [25], [26], [40].…”

“…In [40] (following [25], [26]), two states x and y are defined to be randomized ⊔-trace equivalent whenever ⌊⌊x⌋⌋ f p (w) = ⌊⌊y⌋⌋ f p (w) w ∈ A * 2 . The following proposition guarantees that such equivalence coincides with ≡ B .…”

Compositional bisimulation metric reasoning with Probabilistic Process Calculi

“…Preliminary results show that in essence, a process combinator is uniformly continuous if the combined processes are copied only finitely many times along their evolution [GT14, GT15,Geb15], and more restrictive constraints guarantee the stronger compositional properties of Lipschitz continuity, non-expansiveness and non-extensiveness. By following the divide and congruence aproach [FvGdW06,FvGdW12,GF12,FvG16,CGT16b], formats for compositional properties can be obtained also through a suitable logical characterization of bisimilarity metric, like that in [CGT16a].…”

Logical Characterization of Trace Metrics

“…Finally, it would be interesting to apply the SOS-based decomposition method proposed in [10] to L (resp. L w ) in order to derive congruence formats for the probabilistic strong (resp.…”