We propose a sound and complete compositional proof rule for distributed synthesis. Applying our proof rule only requires the manual strengthening of the specification into a conjunction of formulas that can be guaranteed by individual black-box processes. All premises of the proof rule can be checked automatically. For this purpose, we give an automata-theoretic synthesis algorithm for single processes in distributed architectures. The behavior of the local environment of a process is unknown in the process of synthesis and cannot be assumed to be maximal. We therefore consider reactive environments that have the power to disable some of their own actions, and provide methods for synthesis (and realizability checking) in this setting. We establish upper bounds for CTL (2EXPTIME) and CTL* (3EXPTIME) synthesis with incomplete information, matching the known lower bounds for these problems, and provide matching upper and lower bounds for μ-calculus synthesis (2EXPTIME) with complete or incomplete information. Synthesis in reactive environments is harder than synthesis in maximal environments, where CTL, CTL* and μ-calculus synthesis are EXPTIME, 2EXPTIME and EXPTIME complete, respectively.
A new proof rule for almost-sure termination