Structural Refinement for the Modal nu-Calculus

We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nu-calculus. Using new translations between the modal nu-calculus and disjunctive modal transition systems, we show that these two specification formalisms are structurally equivalent. Using our translations, we also transfer the structural operations of composition and quotient from disjunctive modal transition systems to the modal nu-calculus. This shows that the modal nu-calculus supports composition and decomposition of specifications.Comment: Accepted at ICTAC 201

Tree rules in probabilistic transition system specifications with negative and quantitative premises

Probabilistic transition system specifications (PTSSs) in the ntmufnu/ntmuxnu format provide structural operational semantics for Segala-type systems that exhibit both probabilistic and nondeterministic behavior and guarantee that isimilarity is a congruence.Similar to the nondeterministic case of rule format tyft/tyxt, we show that the well-foundedness requirement is unnecessary in the probabilistic setting. To achieve this, we first define an extended version of the ntmufnu/ntmuxnu format in which quantitative premises and conclusions include nested convex combinations of distributions. This format also guarantees that bisimilarity is a congruence. Then, for a given (possibly non-well-founded) PTSS in the new format, we construct an equivalent well-founded transition system consisting of only rules of the simpler (well-founded) probabilistic ntree format. Furthermore, we develop a proof-theoretic notion for these PTSSs that coincides with the existing stratification-based meaning in case the PTSS is stratifiable. This continues the line of research lifting structural operational semantic results from the nondeterministic setting to systems with both probabilistic and nondeterministic behavior.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

Compositionality of probabilistic Hennessy-Milner logic through structural operational semantics

We present a method to decompose HML formulae for reactive probabilistic processes. This gives rise to a compositional modal proof system for the satisfaction relation of probabilistic process algebras. The satisfaction problem of a probabilistic HML formula for a process term is reduced to the question of whether its subterms satisfy a derived formula obtained via the operational semantics

Compositionality of probabilistic Hennessy-Milner logic through structural operational semantics

We present a method to decompose HML formulae for reactive probabilistic processes. This gives rise to a compositional modal proof system for the satisfaction relation of probabilistic process algebras. The satisfaction problem of a probabilistic HML formula for a process term is reduced to the question of whether its subterms satisfy a derived formula obtained via the operational semantics

Probabilistic Semantics: Metric and Logical Character¨ations for Nondeterministic Probabilistic Processes

In this thesis we focus on processes with nondeterminism and probability in the PTS model, and we propose novel techniques to study their semantics, in terms of both classic behavioral relations and the more recent behavioral metrics. Firstly, we propose a method for decomposing modal formulae in a probabilistic extension of the Hennessy-Milner logic. This decomposition method allows us to derive the compositional properties of probabilistic (bi)simulations. Then, we propose original notions of metrics measuring the disparities in the behavior of processes with respect to (decorated) trace and testing semantics. To capture the differences in the expressive power of the metrics we order them by the relation `makes processes further than'. Thus, we obtain the first spectrum of behavioral metrics on the PTS model. From this spectrum we derive an analogous one for the kernels of the metrics, ordered by the relation `makes strictly less identification than'. Finally, we introduce a novel technique for the logical characterization of both behavioral metrics and their kernels, based on the notions of mimicking formula and distance on formulae. This kind of characterization allows us to obtain the first example of a spectrum of distances on processes obtained directly from logics. Moreover, we show that the kernels of the metrics can be characterized by simply comparing the mimicking formulae of processes