  In this work we study the cost of local and global proofs on distributed
verification. In this setting the nodes of a distributed system are provided
with a nondeterministic proof for the correctness of the state of the system,
and the nodes need to verify this proof by looking at only their local
neighborhood in the system.
  Previous works have studied the model where each node is given its own,
possibly unique, part of the proof as input. The cost of a proof is the maximum
size of an individual label. We compare this model to a model where each node
has access to the same global proof, and the cost is the size of this global
proof.
  It is easy to see that a global proof can always include all of the local
proofs, and every local proof can be a copy of the global proof. We show that
there exists properties that exhibit these relative proof sizes, and also
properties that are somewhere in between. In addition, we introduce a new lower
bound technique and use it to prove a tight lower bound on the complexity of
reversing distributed decision and establish a link between communication
complexity and distributed proof complexity.
