Proof labeling schemes

This paper addresses the problem of locally verifying global properties. Several natural questions are studied, such as "how expensive is local verification?" and more specifically "how expensive is local verification compared to computation?" A suitable model is introduced in which these questions are studied in terms of the number of bits a node needs to communicate. In particular, it is shown that the cost of verification is sometimes rather high, even higher than the number of bits needed for a computation. On the other hand, approaches are presented for the efficient construction of schemes, and upper and lower bounds are established on the cost of schemes for multiple basic problems. The paper also studies the role and cost of unique identities in terms of impossibility and complexity. Previous studies on related questions deal with distributed algorithms that simultaneously compute a configuration and verify that this configuration has a certain desired property. It turns out that this combined approach enables verification to be less costly, since the configuration is typically generated so as to be easily verifiable. In contrast, our approach separates the configuration design from the verification. That is, it first generates the desired configuration without bothering with the need to verify, and then handles the task of constructing a suitable verification scheme. Our approach thus allows for a more modular design of algorithms, and has the potential to aid in verifying properties even when the original design of the structures for maintaining them was done without verification in mind.