2017/06/14 by Lane A. Hemaspaandra, Hemaspaandra, Lane A., David E. Narváez +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced Graph Theory Research #Artificial Intelligence (cs.AI) #Computational Complexity (cs.CC) #F.1.3 #F.4.1 #FOS: Computer and information sciences #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Protein Degradation and Inhibitors #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1706.04582
openalex publication_date 2017/06/14 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
Backdoors and backbones of Boolean formulas are hidden structural properties.\nA natural goal, already in part realized, is that solver algorithms seek to\nobtain substantially better performance by exploiting these structures.\n However, the present paper is not intended to improve the performance of SAT\nsolvers, but rather is a cautionary paper. In particular, the theme of this\npaper is that there is a potential chasm between the existence of such\nstructures in the Boolean formula and being able to effectively exploit them.\nThis does not mean that these structures are not useful to solvers. It does\nmean that one must be very careful not to assume that it is computationally\neasy to go from the existence of a structure to being able to get one's hands\non it and/or being able to exploit the structure.\n For example, in this paper we show that, under the assumption that P \≠\nNP, there are easily recognizable families of Boolean formulas with strong\nbackdoors that are easy to find, yet for which it is hard (in fact,\nNP-complete) to determine whether the formulas are satisfiable. We also show\nthat, also under the assumption P \≠ NP, there are easily recognizable sets\nof Boolean formulas for which it is hard (in fact, NP-complete) to determine\nwhether they have a large backbone.\n