2 research outputs found
Quantified Conjunctive Queries on Partially Ordered Sets
We study the computational problem of checking whether a quantified
conjunctive query (a first-order sentence built using only conjunction as
Boolean connective) is true in a finite poset (a reflexive, antisymmetric, and
transitive directed graph). We prove that the problem is already NP-hard on a
certain fixed poset, and investigate structural properties of posets yielding
fixed-parameter tractability when the problem is parameterized by the query.
Our main algorithmic result is that model checking quantified conjunctive
queries on posets of bounded width is fixed-parameter tractable (the width of a
poset is the maximum size of a subset of pairwise incomparable elements). We
complement our algorithmic result by complexity results with respect to classes
of finite posets in a hierarchy of natural poset invariants, establishing its
tightness in this sense.Comment: Accepted at IPEC 201