Parameterized Synthesis

We study the synthesis problem for distributed architectures with a parametric number of finite-state components. Parameterized specifications arise naturally in a synthesis setting, but thus far it was unclear how to detect realizability and how to perform synthesis in a parameterized setting. Using a classical result from verification, we show that for a class of specifications in indexed LTLX, parameterized synthesis in token ring networks is equivalent to distributed synthesis in a network consisting of a few copies of a single process. Adapting a well-known result from distributed synthesis, we show that the latter problem is undecidable. We describe a semi-decision procedure for the parameterized synthesis problem in token rings, based on bounded synthesis. We extend the approach to parameterized synthesis in token-passing networks with arbitrary topologies, and show applicability on a simple case study. Finally, we sketch a general framework for parameterized synthesis based on cutoffs and other parameterized verification techniques.