Treewidth-Aware Cycle Breaking for Algebraic Answer Set Counting

Probabilistic reasoning, parameter learning, and most probable explanation inference for answer set programming have recently received growing attention. They are only some of the problems that can be formulated as Algebraic Answer Set Counting (AASC) problems. The latter are however hard to solve, and efficient evaluation techniques are needed. Inspired by Vlasser et al.'s Tp-compilation (JAR, 2016), we introduce Tp-unfolding, which employs forward reasoning to break the cycles in the positive dependency graph of a program by unfolding them. Tp-unfolding is defined for any normal answer set program and unfolds programs with respect to unfolding sequences, which are akin to elimination orders in SAT-solving. Using "good" unfolding sequences, we can ensure that the increase of the treewidth of the unfolded program is small. Treewidth is a measure adhering to a program's tree-likeness, which gives performance guarantees for AASC. We give sufficient conditions for the existence of good unfolding sequences based on the novel notion of component-boosted backdoor size, which measures the cyclicity of the positive dependencies in a program. The experimental evaluation of a prototype implementation, the AASC solver aspmc, shows promising results.