Probabilistic Semantics: Metric and Logical Character\ua8ations 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

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

Multi-scale modelling of biological systems in process algebra

There is a growing interest in combining different levels of detail of biological phenomena into unique multi-scale models that represent both biochemical details and higher order structures such as cells, tissues or organs. The state of the art of multi-scale models presents a variety of approaches often tailored around specific problems and composed of a combination of mathematical techniques. As a result, these models are difficult to build, compose, compare and analyse. In this thesis we identify process algebra as an ideal formalism to multi-scale modelling of biological systems. Building on an investigation of existing process algebras, we define process algebra with hooks (PAH), designed to be a middle-out approach to multi-scale modelling. The distinctive features of PAH are: the presence of two synchronisation operators, distinguishing interactions within and between scales, and composed actions, representing events that occur at multiple scales. A stochastic semantics is provided, based on functional rates derived from kinetic laws. A parametric version of the algebra ensures that a model description is compact. This new formalism allows for: unambiguous definition of scales as processes and interactions within and between scales as actions, compositionality between scales using a novel vertical cooperation operator and compositionality within scales using a traditional cooperation operator, and relating models and their behaviour using equivalence relations that can focus on specified scales. Finally, we apply PAH to define, compose and relate models of pattern formation and tissue growth, highlighting the benefits of the approach

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum