We define and study the model of patterned non-determinism in bipartite communication complexity, denoted by $PNP^{X\leftrightarrow Y}$. It generalises the known models $UP^{X\leftrightarrow Y}$ and $FewP^{X\leftrightarrow Y}$ through relaxing the constraints on the witnessing structure of the underlying $NP^{X\leftrightarrow Y}$-protocol. It is shown that for the case of total functions $PNP^{X\leftrightarrow Y}$ equals $P^{X\leftrightarrow Y}$ (similarly to $UP^{X\leftrightarrow Y}$ and $FewP^{X\leftrightarrow Y}$). Moreover, the corresponding exhaustive witness-searching problem -- determining the full set of witnesses that lead to the acceptance of a given input pair -- also has an efficient deterministic protocol. The possibility of efficient exhaustive $PNP^{X\leftrightarrow Y}$-search is used to analyse certain three-party communication regime (under the "number in hand" input partition): The corresponding three-party model is shown to be as strong qualitatively as the weakest among its two-party amplifications obtained by allowing free communication between a pair of players.

翻译：本文定义并研究了二分通信复杂度中的模式化非确定性模型，记为$PNP^{X\leftrightarrow Y}$。该模型通过放宽底层$NP^{X\leftrightarrow Y}$协议中见证结构的约束条件，推广了已知的$UP^{X\leftrightarrow Y}$和$FewP^{X\leftrightarrow Y}$模型。研究表明，对于全函数情形，$PNP^{X\leftrightarrow Y}$等于$P^{X\leftrightarrow Y}$（类似于$UP^{X\leftrightarrow Y}$和$FewP^{X\leftrightarrow Y}$）。此外，相应的穷举见证搜索问题——即确定导致给定输入对被接受的全部见证集——同样存在高效的确定性协议。利用$PNP^{X\leftrightarrow Y}$搜索的穷举高效性，本文进一步分析了特定的三方通信机制（基于“手中数字”输入划分）：该三方模型被证明在定性强度上等价于通过允许某对玩家自由通信所获得的任意两方放大模型中的最弱类型。