Characterizing Structural Hardness of Logic Programs: What Makes Cycles and Reachability Hard for Treewidth?

Answer Set Programming (ASP) is a problem modeling and solving framework for several problems in KR with growing industrial applications. Also studies of computational complexity deeper insights into the hardness its sources, ASP has been attracting researchers many years. These resulted fruitful characterizations terms classes, fine-grained form dichotomy-style results, as well detailed parameterized landscapes. Recently, this lead to novel result establishing that measure treewidth, which captures structural density program, evaluation well-known class normal programs expected be slightly harder than deciding satisfiability (SAT). However, it unclear how utilize power ASP. This paper deals reduction from SAT goes beyond encodings: We explicitly ASP, whereby we sublinearly decrease probably cannot significantly improved. Then, compared existing characterizes way by required functional dependency graph’s cycle length (SCC size) on treewidth.