IncrementalWFOMC3: A Fast Algorithm for Two-Variable Logic with Counting and Modulo Counting
A new algorithm, IncrementalWFOMC3, has been developed by researchers for weighted first-order model counting (WFOMC) specifically targeting the two-variable fragment with counting quantifiers (C²) and its modulo counting variant (C²_mod). WFOMC plays a crucial role in lifted probabilistic inference by calculating the weighted total of all models represented by a first-order sentence within a finite domain. While C² is recognized as one of the most expressive domain-liftable fragments, current methods depend on multi-stage reductions that remove counting quantifiers through cardinality constraints, leading to significant inefficiencies as the domain expands. IncrementalWFOMC3 circumvents these reductions, providing a more effective solution. This research is documented on arXiv with the ID 2605.03391.
Key facts
- IncrementalWFOMC3 is a lifted algorithm for WFOMC on C² and C²_mod.
- WFOMC computes weighted sum of all models of a first-order sentence over a finite domain.
- C² is a two-variable fragment with counting quantifiers.
- C²_mod is the modulo counting extension of C².
- Existing algorithms for C² use multi-stage reductions with cardinality constraints.
- Reductions introduce substantial overhead as domain size grows.
- IncrementalWFOMC3 avoids reduction techniques.
- Paper published on arXiv with ID 2605.03391.
Entities
Institutions
- arXiv