ProPPA

Abstract

Formal languages like process algebras have been shown to be e ective tools in modelling a wide range of dynamic systems, providing a high-level description that is readily transformed into an executable model. However their application is sometimes hampered because the quantitative details of many real-world systems of interest are not fully known. In contrast, in machine learning there has been work to develop probabilistic programming languages, which provide system descriptions that incorporate uncertainty and leverage advanced statistical techniques to infer unknown parameters from observed data. Unfortunately current probabilistic programming languages are typically too low-level to be suitable for complex modelling. In this paper we present ProPPA, the rst instance of the probabilistic programming paradigm being applied to a high-level, formal language, and its supporting tool suite. We explain the semantics of the language in terms of a quantitative generalisation of Constraint Markov Chains and describe the implementation of the language, discussing in some detail the di erent inference algorithms available, and their domain of applicability. We conclude by illustrating the use of the language on simple but non-trivial case studies: here ProPPA is shown to combine the elegance and simplicity of high-level formal modelling languages with an e ective way of incorporating data, making it a promising tool for modelling studies. CCS Concepts: • Computing methodologies → Modeling methodologies; Uncertainty quanti cation; • Mathematics of computing → Markov processes; Bayesian computation; Markov-chain Monte Carlo methods;

Stochastic process algebras and their markovian semantics

“…Using inference, the model may be combined with the observations to derive updated probability distributions, over the CTMCs and over rates [Georgoulas et al 2017]. Currently observations may be collected either as time series values of population values in a model, or as temporal logic formulas that express constraints on the observed behaviours [Georgoulas et al 2018].…”

“…In this setting the semantic object corresponding to the SPA model is no longer a single CTMC, but a Probabilistic Constraint Markov Chain [Georgoulas et al 2018]: -S is the set of states, of cardinality k.…”

“…In the case of PCMC we generalise CTMCs in an analogous way, but additionally capture information about the likelihood of different values that satisfy the constraints by associating a probability distribution with the satisfaction set. A structured operational semantics, derived in the FuTS style [De Nicola et al 2013], is presented in [Georgoulas et al 2018].…”