Final Report Summary - EQUALIS (EQualIS : Enhancing the Quality of Interacting Systems) The ubiquitous use of computerized systems, and their increasing complexity, demand formal evidences of their correctness. While current formal-verification techniques have already been applied to a number of case studies, they are not sufficient yet to fully analyze several aspects of complex systems such as communication networks, embedded systems or industrial controllers. Several characteristics are in particular not properly taken into account so far, including the rich interaction between components, the imprecisions inherent to systems evolving in a (digital or physical) environment, and quantitative constraints that are given for instance by limited resources. The goal of the EQualIS project is to develop a rich framework to design and analyze such systems.As a first outcome of the project lies a comprehensive study of rich logical formalisms allowing to express complex interactions between components: computational issues are important, but so are semantical issues, which require a foremost care! Simple interaction cases include Nash equilibria, for which we have developed efficient algorithms, even in a context with limited communication between agents (though in a deterministic setting).A very important challenge in the development of embedded or industrial controllers is that of robustness, which ensures the expected properties, even under small perturbations in the execution of the system. Those imprecisions may be due to internal imprecisions or to (e.g. physical) interaction with the environment. Important achievements of the EQualIS project include synthesis algorithms for time-dependent controllers which are robust to slight timing perturbations: the synthesized controller will behave correctly even if delays are slightly perturbed.An important part of the project is dedicated to the evaluation of the quality of the system, with regards to specified quality evaluation criteria. While some of our results show that this is very hard to give strong evidence of the quality of a computerized system, an important achievement of the project is the development of alternative approaches like: (1) the development of monitoring or diagnosis algorithms (monitor the system online and raise an alarm if an unexpected event occurs); (2) the investigation of the dynamic complexity paradigm (when updating a model, find a non-expensive way to update the result of the analysis); and (3) the design of approximation algorithms to circumvent the unfeasibility results (approximated algorithms or almost-optimal solutions, are sufficient in practice, hence this is a fairly interesting approach for the analysis of really complex systems).Finally, in the EQualIS project, we demonstrated that technics from formal methods could be used in connex fields like motion planning problems or smart grids, yielding solutions (controllers) with guarantees. We also investigated further more standard controller synthesis problems, with interesting new solutions. All these applications made use of many of the aspects (with sometimes a more pragmatic approach) that we theoretically studied in other parts of the project. We also developed a tool TiAMo for the analysis of weighted timed automata.
