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 decide realizability and how to perform synthesis. Using a classical result from verification, we show that for specifications in LTL\X, parameterized synthesis of token ring networks is equivalent to distributed synthesis of a network consisting of a few copies of a single process. Adapting a result from distributed synthesis, we show that the latter problem is undecidable. We then describe a semi-decision procedure based on bounded synthesis and show applicability on a simple case study. Finally, we sketch a general framework for parameterized synthesis based on cut-off results for verification.