Abstract
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.
This work was supported by JSPS KAKENHI JP16K05255.
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Acknowledgement
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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Suzuki, T. (2020). Communication Interruption Between a Game Tree and Its Leaves. In: Ao, SI., Kim, H., Castillo, O., Chan, As., Katagiri, H. (eds) Transactions on Engineering Technologies. IMECS 2018. Springer, Singapore. https://doi.org/10.1007/978-981-32-9808-8_15
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DOI: https://doi.org/10.1007/978-981-32-9808-8_15
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