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2011
ACM

Locally checkable proofs

8 years 2 months ago
Locally checkable proofs
This work studies decision problems from the perspective of nondeterministic distributed algorithms. For a yes-instance there must exist a proof that can be verified with a distributed algorithm: all nodes must accept a valid proof, and at least one node must reject an invalid proof. We focus on locally checkable proofs that can be verified with a constant-time distributed algorithm. For example, it is easy to prove that a graph is bipartite: the locally checkable proof gives a 2-colouring of the graph, which only takes 1 bit per node. However, it is more difficult to prove that a graph is not bipartite—it turns out that any locally checkable proof requires Ω(log n) bits per node. In this work we classify graph problems according to their local proof complexity, i.e., how many bits per node are needed in a locally checkable proof. We establish tight or near-tight results for classical graph properties such as the chromatic number. We show that the proof complexities form a natura...
Mika Göös, Jukka Suomela
Added 17 Sep 2011
Updated 17 Sep 2011
Type Journal
Year 2011
Where PODC
Authors Mika Göös, Jukka Suomela
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