Theoretical Foundations of Advanced Synthesis

The rapid development of complex and safety-critical systems requires reliable verification methods. In automated synthesis, we transform a specification into a correct-by-construction system. In recent years, there have been significant advances in the algorithmic front of synthesis. Still, the integration of synthesis in industry has been slow. This project addresses two critical reasons why synthesis has been hindered. First, while verification offers designers a tool to check their designs, synthesis aims to replace manual design. Designers will give up manual design only after being convinced that the automatic process replacing it indeed generates systems of comparable quality, which current definitions of synthesis ignores. Second, designers can cope manually with simple settings. Thus, automated synthesis is needed in complex settings, which are not covered by current definitions of the problem.My overarching objective is to develop the theoretical foundations of advanced synthesis, namely the next generation of synthesis concepts and algorithms, taking into account the complex settings in which synthesis is needed and the many considerations that are abstracted in current definitions of the problem. I will formalize and study the following three aspects of advanced synthesis: (1) Quality and complexity measures: behavioral quality as well as complexity measures that refer to resources needed by the synthesized system. (2) Game-theoretic considerations: settings with components that may or may not collaborate in order to cooperatively or selfishly achieve individual and common objectives. (3) Evolving and unpredictable environments: behavioral, structural, and conceptual assumptions on the environment. The research will be based on clean mathematical foundations and will combine the above methodological contributions with advances in the theory and applications of automata on infinite objects.