An AND-OR-Tree Connected to Leaves via Communication Channels - Suzuki, Toshio (Lecture notes in engineering and computer science, 2018)
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. A key to the proof is Riemann zeta function.