  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
