Ranked Enumeration for MSO on Trees via Knowledge Compilation

Antoine Amarilli (1, 2) , Pierre Bourhis (3, 4) , Florent Capelli (5) , Mikaël Monet (6)

1 DIG - Data, Intelligence and Graphs
2 INFRES - Département Informatique et Réseaux
3 SPIRALS - Self-adaptation for distributed services and large software systems
4 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
5 CRIL - Centre de Recherche en Informatique de Lens
6 LINKS - Linking Dynamic Data

We study the problem of enumerating the satisfying assignments for circuit classes from knowledge compilation, where assignments are ranked in a specific order. In particular, we show how this problem can be used to efficiently perform ranked enumeration of the answers to MSO queries over trees, with the order being given by a ranking function satisfying a subset-monotonicity property. Assuming that the number of variables is constant, we show that we can enumerate the satisfying assignments in ranked order for so-called multivalued circuits that are smooth, decomposable, and in negation normal form (smooth multivalued DNNF). There is no preprocessing and the enumeration delay is linear in the size of the circuit times the number of values, plus a logarithmic term in the number of assignments produced so far. If we further assume that the circuit is deterministic (smooth multivalued d-DNNF), we can achieve linear-time preprocessing in the circuit, and the delay only features the logarithmic term.

Keywords: knowledge compilation; monadic second-order logic; 2012 ACM Subject Classification Information systems → Relational database model phrases Enumeration knowledge compilation monadic second-order logic Digital Object Identifier 10.4230/LIPIcs; 2012 ACM Subject Classification Information systems → Relational database model phrases Enumeration

Domains: Computer Science [cs]

Antoine Amarilli, Pierre Bourhis, Florent Capelli, Mikaël Monet. Ranked Enumeration for MSO on Trees via Knowledge Compilation. 2023. ⟨hal-04377344⟩