Encoding Constraints as Binary Constraint Networks Satisfying BTP

Recently, the Binary Constraint Tree (BCT), a tree structured Binary Constraint Network (BCN), has been shown to be more succinct than various ad-hoc constraints. In this paper, we investigate the modelling power of a well-known tractable hybrid class generalizing BCT, i.e. the class of BCNs satisfying Broken Triangle Property (BTP) called BTP Networks (BTPNs). We show that the consistency checker of BTPN can be computed by polysize monotone circuit, thus, some global constraints cannot be encoded as polysize BTPN, such as the AllDifferent and Linear constraints. Then our study reveals that BTPN is strictly more succinct than the DNNF constraint and all 14 ad-hoc constraints discussed in (Wang and Yap 2023), such as the context-free grammar, BCT and smart table constraints. Furthermore, we also show that BTPN is as powerful as DNNF in terms of computing various operations and queries. In addition, we prove that it is NP-hard to determine the minimum sized BTPN encoding a constraint.