Church's synthesis problem asks whether there exists a finite-state stream transducer satisfying a given input-output specification. For specifications written in Monadic Second-Order Logic (MSO) over infinite words, Church's synthesis can theoretically be solved algorithmically using automata and games. We revisit Church's synthesis via the Curry-Howard correspondence by introducing SMSO, an intuitionistic variant of MSO over infinite words, which is shown to be sound and complete w.r.t. synthesis thanks to an automata-based realizability model.

@article{paperbot739,
  title = {A Curry-Howard Approach to Church's Synthesis},
  author = {Cécilia Pradic and Colin Riba},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 15, Issue 4},
  year = {2019},
  doi = {10.23638/lmcs-15(4:13)2019}
}