On Computing Generalized Backbones

Abstract

The concept of backbone variables, i.e., variables that take the same value in all solutions-or, equivalently, never take a specific value-finds various important applications in the context of Boolean satisfiability (SAT), motivating the development of efficient algorithms for determining the set of backbone variables of a given propositional formula. Notably, this problem surpasses the complexity of merely deciding satisfiability. In this work we consider generalizations of the concept of backbones in SAT to non-binary (and potentially infinite) domain constraint satisfaction problems. Specifically, we propose a natural generalization of backbones to the context of satisfiability modulo theories (SMT), applicable to a range of different theories as well as CSPs in general, and provide two generic algorithms for determining the backbone in this general context. As two concrete instantiations, we focus on two central SMT theories, the theory of linear integer arithmetic (LIA) with infinite integer domains, and the theory of bit vectors (BV), and empirically evaluate the potential of the proposed algorithms on both LIA and BV instances.

A preference-based approach to backbone computation with application to argumentation

“…In the context of CSPs, a notion of backbones has been proposed under the name of frozen/fixable variables [6,10,27], defined as variables that take the same value in all solutions. A more general notion is that of generalized backbones [39], which extends backbones to arbitrary variable domains and thereby to, e.g., the satisfiability modulo theories approach (SMT). Backbones also have connections to minimal constraint networks [19] and minimal labelings in qualitative constraints networks [2].…”