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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2502.02022 |
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| _version_ | 1866929697200275456 |
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| author | Alhamdan, Yousef M. |
| author_facet | Alhamdan, Yousef M. |
| contents | We study a decision tree model in which one is allowed to query subsets of variables. This model is a generalization of the standard decision tree model. For example, the $\lor-$decision (or $T_1$-decision) model has two queries, one is a bit-query and one is the $\lor$-query with arbitrary variables. We show that a monotone property graph, i.e. nontree graph is lower bounded by $n\log n$ in $T_1$-decision tree model. Also, in a different but stronger model, $T_2$-decision tree model, we show that the majority function and symmetric function can be queried in $\frac{3n}{4}$ and $n$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02022 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper and Lower Bounds on $T_1$ and $T_2$ Decision Tree Model Alhamdan, Yousef M. Computational Complexity We study a decision tree model in which one is allowed to query subsets of variables. This model is a generalization of the standard decision tree model. For example, the $\lor-$decision (or $T_1$-decision) model has two queries, one is a bit-query and one is the $\lor$-query with arbitrary variables. We show that a monotone property graph, i.e. nontree graph is lower bounded by $n\log n$ in $T_1$-decision tree model. Also, in a different but stronger model, $T_2$-decision tree model, we show that the majority function and symmetric function can be queried in $\frac{3n}{4}$ and $n$, respectively. |
| title | Upper and Lower Bounds on $T_1$ and $T_2$ Decision Tree Model |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2502.02022 |