Abstract. We extend the notion of distributed decision in the framework of distributed network computing, inspired by recent results on so-called distributed graph automata. We show that, by using distributed decision mechanisms based on the interaction between a prover and a disprover, the size of the certificates distributed to the nodes for certifying a given network property can be drastically reduced. For instance, we prove that minimum spanning tree can be certified with O(log n)-bit certificates in n-node graphs, with just one interaction between the prover and the disprover, while it is known that certifying MST requires Ω(log 2 n)-bit certificates if only the prover can act. The improvement can even be exponential for some simple graph properties. For instance, it is known that certifying the existence of a nontrivial automorphism requires Ω(n 2 ) bits if only the prover can act. We show that there is a protocol with two interactions between the prover and the disprover enabling to certify nontrivial automorphism with O(log n)-bit certificates. These results are achieved by defining and analysing a local hierarchy of decision which generalizes the classical notions of proof-labelling schemes and locally checkable proofs. * The first and second authors received additional support from ANR project DISPLEXITY, and from INRIA project GANG.
Recently, a hierarchy of local decision as an interaction between a prover and a disprover was presented in REF .
A hierarchy of local decision
ArXiv
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Computer Science