The Opacity of Backbones

No. 1: Thirty-First AAAI Conference On Artificial Intelligence

Volume

Proceedings of the AAAI Conference on Artificial Intelligence, 31

Main Track: Search and Constraint Satisfaction

A backbone of a boolean formula F is a collection S of its variables for which there is a unique partial assignment aS such that F[aS] is satisfiable (Monasson et al. 1999; Williams, Gomes, and Selman 2003). ÊThis paper studies the nontransparency of backbones. ÊWe show that, under the widely believed assumption that integer factoring is hard, there exist sets of boolean formulas that have obvious, nontrivial backbones yet finding the values, aS, of those backbones is intractable. ÊWe also show that, under the same assumption, there exist sets of boolean formulas that obviously have large backbones yet producing such a backbone S is intractable. ÊFurther, we show that if integer factoring is not merely worst-case hard but is frequently hard, as is widely believed, then the frequency of hardness in our two results is not too much less than that frequency.

10.1609/aaai.v31i1.11134