Communication Interruption Between a Game Tree and Its Leaves
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We introduce a successor model of an AND-OR tree. Leaves are connected to internal nodes via communication channels that possibly have high probability of interruption. By depth-first communication we mean the following protocol: if a given algorithm probes a leaf then it continues to make queries to that leaf until return of an answer. For each such tree, we give a concrete example of interruption probability setting with the following property. For any independent and identical distribution on the truth assignments (probability is assumed to be neither 0 nor 1), any depth-first search algorithm that performs depth-first communication is not optimal. This result makes sharp contrast with the counterpart on the usual AND-OR tree (Tarsi) that optimal and depth-first algorithm exists. Our concrete example is based on Riemann zeta function. We also present a generalized framework.
KeywordsAND-OR tree Depth-first algorithm Directional algorithm Optimal algorithm Communication channel Communication interruption Riemann zeta function Independent and identical distribution
We are grateful to the anonymous referees of the previous version for helpful advices. We wish to thank the attendants of IMECS 2018 for valuable discussion.
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