Randomized proof-labeling schemes

Proof-labeling schemes, introduced by Korman, Kutten and Peleg [PODC 2005], are a mechanism to certify that a network configuration satisfies a given boolean predicate. Such mechanisms find applications in many contexts, e.g., the design of fault-tolerant distributed algorithms. In a proof-labeling scheme, predicate verification consists of neighbors exchanging labels, whose contents depends on the predicate. In this paper, we introduce the notion of randomized proof-labeling schemes where messages are randomized and correctness is probabilistic. We show that randomization reduces label size exponentially while guaranteeing probability of correctness arbitrarily close to one. In addition, we present a novel label-size lower bound technique that applies to both deterministic and randomized proof-labeling schemes. Using this technique, we establish several tight bounds on the verification complexity of MST, acyclicity, connectivity, and longest cycle size.