Brief Announcement: Space-Time Tradeoffs for Distributed Verification

Verifying that a network configuration satisfies a given boolean predicate is a fundamental problem in distributed computing. Many variations of this problem have been studied, for example, in the context of proof labeling schemes (PLS), locally checkable proofs (LCP), and non-deterministic local decision (NLD). In all of these contexts, verification time is assumed to be constant. Korman, Kutten and Masuzawa presented a proof-labeling scheme for MST, with poly-logarithmic verification time, and logarithmic memory at each vertex. In this paper we introduce the notion of a t-PLS, which allows the verification procedure to run for super-constant time. Our work analyzes the tradeoffs of t-PLS between time, label size, message length, and computation space. We construct a universal t-PLS and prove that it uses the same amount of total communication as a known one-round universal PLS, and t factor smaller labels. In addition, we provide a general technique to prove lower bounds for space- time tradeoffs of t-PLS. We use this technique to show an optimal tradeoff for testing that a network is acyclic (cycle free). Our optimal t-PLS for acyclicity uses label size and computation space O((log n)/t). We further describe a recursive O(log* n) space verifier for acyclicity which does not assume previous knowledge of the run-time t.