Dichotomy theorems, which characterize the conditions under which a problem can be solved efficiently, have helped identify important tractability borders for as probabilistic query evaluation, view maintenance, query containment (among many more problems). However, dichotomy theorems for many such problems remain elusive under key settings such as bag semantics or for queries with self-joins. This work aims to unearth dichotomies for fundamental problems in reverse data management and knowledge representation. We use a novel approach to discovering dichotomies: instead of creating dedicated algorithms for easy (PTIME) and hard cases (NP-complete), we devise unified algorithms that are guaranteed to terminate in PTIME for easy cases. Using this approach, we discovered new tractable cases for the problem of minimal factorization of provenance formulas as well as dichotomies under bag semantics for the problems of resilience and causal responsibility

翻译：二分定理描述了问题可被高效求解的条件，有助于识别诸如概率查询评估、视图维护、查询包含（以及许多其他问题）等重要问题的可处理性边界。然而，在关键设置下（如元组包语义或含自连接的查询），许多此类问题的二分定理仍难以获得。本研究旨在揭示逆向数据管理与知识表示中基础问题的二分性质。我们采用一种新颖的二分发现方法：不再为易处理情况（PTIME）与困难情况（NP完全）分别设计专用算法，而是设计统一的算法，确保其对于易处理情况能在多项式时间内终止。利用该方法，我们发现了来源公式最小因子分解问题的新可处理情况，以及在元组包语义下弹性与因果责任问题的二分性质。