What Can Be Verified Locally?
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
JOURNAL OF COMPUTER AND SYSTEM SCIENCES, Volume 97
AbstractIn the framework of distributed network computing, it is known that not all Turing-decidable predicates on labeled networks can be decided locally whenever the computing entities are Turing machines (TM). This holds even if nodes are running non-deterministic Turing machines (NTM). In contrast, we show that every Turing-decidable predicate on labeled networks can be decided locally if nodes are running alternating Turing machines (ATM). More specifically, we show that, for every such predicate, there is a local algorithm for ATMs, with at most two alternations, that decides whether the actual labeled network satisfies that predicate. To this aim, we define a hierarchy of classes of decision tasks, where the lowest level contains tasks solvable with TMs, the first level those solvable with NTMs, and the level k>1 contains those tasks solvable with ATMs with k-1 alternations. We characterize the entire hierarchy, and show that it collapses in the second level.
Distributed computing, Decision problems, Local model
Balliu , A , D'Angelo , G , Fraigniaud , P & Olivetti , D 2018 , ' What Can Be Verified Locally? ' , JOURNAL OF COMPUTER AND SYSTEM SCIENCES , vol. 97 , pp. 106-120 . https://doi.org/10.1016/j.jcss.2018.05.004