In Pliable Private Information Retrieval (PPIR) with a single server, messages are partitioned into $\Gamma$ non-overlapping classes. The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. In S. A. Obead, H. Y. Lin and E. Rosnes, Single-Server Pliable Private Information Retrieval With Side Information, arXiv:2305.06857, authors consider the problem of PPIR with Side Information (PPIR-SI), where the user now has side information. The user wants to retrieve any new message (not included in the side information) from its desired class without revealing the identity of the desired class and its side information. A scheme for the PPIR-SI is given by Obead et al. for the case when the users side information is unidentified, and this case is referred to as PPIR with Unidentifiable SI (PPIR-USI). In this paper, we study the problem of PPIR for the single server case when the side information is partially identifiable, and we term this case as PPIR with Identifiable Side Information (PPIR-ISI). The user is well aware of the identity of the side information belonging to $\eta$ number of classes, where $1\leq \eta \leq \Gamma$. In this problem, The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. We give a scheme for PPIR-ISI, and we prove that having identifiable side information is advantageous by comparing the rate of the proposed scheme to the rate of the PPIR-USI scheme given by Obead et al. for some cases. Further, we extend the problem of PPIR-ISI for multi-user case, where users can collaborately generate the query sets, and we give a scheme for this problem.

翻译：在具有单个服务器的可塑性私密信息检索（PPIR）中，消息被划分为$\Gamma$个不重叠的类别。用户希望从其目标类别中检索一条消息，同时不向服务器泄露目标类别的身份。在S. A. Obead、H. Y. Lin和E. Rosnes的《Single-Server Pliable Private Information Retrieval With Side Information》（arXiv:2305.06857）一文中，作者考虑了带侧信息的PPIR（PPIR-SI）问题，其中用户拥有侧信息。用户希望从其目标类别中检索任何一条新消息（不在侧信息中），同时不泄露目标类别的身份及其侧信息。当用户的侧信息不可识别时，Obead等人给出了一种PPIR-SI方案，这种情况被称为具有不可识别侧信息的PPIR（PPIR-USI）。本文研究侧信息部分可识别情况下的单服务器PPIR问题，我们将这种情况称为具有可识别侧信息的PPIR（PPIR-ISI）。用户完全知晓属于$\eta$个类别的侧信息的身份，其中$1\leq \eta \leq \Gamma$。在此问题中，用户希望从其目标类别中检索一条消息，同时不向服务器泄露目标类别的身份。我们给出了一种PPIR-ISI方案，并通过将所提方案的速率与Obead等人给出的PPIR-USI方案速率进行对比，证明在某些情况下具有可识别侧信息是有优势的。此外，我们将PPIR-ISI问题扩展到多用户场景，其中用户可以协作生成查询集，并针对该问题给出了一种方案。