  Synthesis of distributed protocols is a hard, often undecidable, problem.
Completion techniques provide partial remedy by turning the problem into a
search problem. However, the space of candidate completions is still massive.
In this paper, we propose optimization techniques to reduce the size of the
search space by a factorial factor by exploiting symmetries (isomorphisms) in
functionally equivalent solutions. We present both a theoretical analysis of
this optimization as well as empirical results that demonstrate its
effectiveness in synthesizing both the Alternating Bit Protocol and Two Phase
Commit. Our experiments show that the optimized tool achieves a speedup of
approximately 2 to 10 times compared to its unoptimized counterpart.
