Final Report Summary - GALE (Games and Automata for Logic Extensions)
A major achievement was the development of the theory of regular cost functions, an extension of regular languages to a quantitative setting that enjoy many of the good properties of the classical cases. Regular cost functions have been developed over finite words, infinite words, finite trees, and partially infinite trees (a standard tool in the verification of hardware devices interacting with the environment for instance). The results can be used as a toolbox for deciding properties involving optimization such as bounding of fixpoints iterations, or constraining consumption of systems. The project has both developed the theory, potential applications in the field of databases or automata theory, and extensions.
Other achievements, among others, involve the precise analysis of quantitative models of automata, that can be used for very accurately estimating the termination time of pieces of program, the fine understanding of logics over linear orders (that are good for representing time), or results on data languages that can be used to model some databases or system logs where many agents interact.