While methods of software validation and verification are by now well established, the approach of automatic synthesis of software (and hardware) is as yet only developed in quite rudimentary form. Algorithmic program synthesis is possible in restricted scenarios, in particular in reactive multi-agent systems with low data complexity and in control systems. Central issues are the establishment of system models that support algorithmic solutions, the combination of discrete and continuous parameters (in hybrid systems), and the exploration of applications. The aim of the Research Training Group AlgoSyn is to unify the expertise from computer science, mathematics, and four engineering disciplines (processor architectures, automatic control, process control engineering, train traffic systems), in order to push forward the desired integration of methods.