QUANTICOL - A quantitative approach to management and design of collective and adaptive behaviours

This final Deliverable of Work Package 3 describes the main achievements obtained during the last reporting period for all three tasks of the work package (and in part during the second reporting period regarding Task 1.3) concerning the development of the theoretical foundations of novel, scalable and spatial formal analysis techniques and the underlying theories to support the design of large scale CAS. During the first two reporting periods of the project a number of innovative analysis techniques have been developed that are highly scalable. Some of these are based on mean field approximation techniques, others involve statistical model checking and machine learning techniques. For all these cases additional model reduction techniques have been developed to further improve scalability of analysis, for example to reduce the number of ordinary differential equations (ODEs) that need to be solved or the number of populations that need to be considered. For what concerns spatial verification several spatial and spatio-temporal logics have been developed for which efficient verification techniques have been created based on model checking and monitoring techniques. In particular, Spatial Logic for Closure Spaces (SLCS), based on the formal framework of closure spaces, and Spatial Signal Temporal Logic (SSTL) extending Signal Temporal Logic (STL) with some of the spatial operators from SLCS in a monitoring setting. Finally, suitable extensions of a software product line engineering (SPLE) approach for CAS were developed, among which family-based verification of behavioural aspects of CAS. In the third and final reporting period all these techniques have been further extended and some combined, implemented and applied to the case studies of the project. Some of the main achievements are: the extension of the fluid model checking algorithms incorporating various kinds of rewards (or costs); study of the conditions under which continuous time population models can be analysed based on discrete time mean field model checking techniques; approximation of probabilistic reachability; development of a front-end language for FlyFast to deal with components and predicate-based interaction; extension of SLCS with temporal operators and with collective operators; combination of statistical and spatio-temporal model checking; application of an extended version of SLCS on Medical Imaging; combination of SSTL with machine learning; development of CTMC and ODE based behavioural equivalences for CAS and related minimisation algorithms; definition of an efficient family-based model checking procedure for SPLE models; development of a tool for quantitative analysis of probabilistic and dynamically reconfigurable SPLE models via statistical model checking; variability-aware software performance models. All these developments are briefly described in the three main sections of this deliverable reflecting the three tasks of Work Package 3.