Space-Time Tradeoffs for Distributed Verification
Rafail Ostrovsky, Mor Perry, Will RosenbaumAbstract:
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 et al.  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, lable size, message length, and computation space. we construct a universal t-PLS and prove that is uses the same amount of total communication as known one-round universal PLS, and t factor smaller tables. In addition, we provide a general technique to prove lower bounds for space-tme tradeoffs of t-PLS. We use this technique to show an optimal tradoff for testing that a network is acyclic ( cycle free). Our optimal t-PLS for acyclicity uses label size and computation space Ο)log n)/t). We further describe a recursive Ο(log∗n) Space verifier for acyclicity which does not assume previous knowledge of the run-time t.
comment: SIROCCO 2017: 53-70
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