Recursive Backdoors for SAT

Authors Nikolas Mählmann , Sebastian Siebertz , Alexandre Vigny

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Author Details

Nikolas Mählmann
  • University of Bremen, Germany
Sebastian Siebertz
  • University of Bremen, Germany
Alexandre Vigny
  • University of Bremen, Germany

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Nikolas Mählmann, Sebastian Siebertz, and Alexandre Vigny. Recursive Backdoors for SAT. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 73:1-73:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


A strong backdoor in a formula φ of propositional logic to a tractable class C of formulas is a set B of variables of φ such that every assignment of the variables in B results in a formula from C. Strong backdoors of small size or with a good structure, e.g. with small backdoor treewidth, lead to efficient solutions for the propositional satisfiability problem SAT. In this paper we propose the new notion of recursive backdoors, which is inspired by the observation that in order to solve SAT we can independently recurse into the components that are created by partial assignments of variables. The quality of a recursive backdoor is measured by its recursive backdoor depth. Similar to the concept of backdoor treewidth, recursive backdoors of bounded depth include backdoors of unbounded size that have a certain treelike structure. However, the two concepts are incomparable and our results yield new tractability results for SAT.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Theory of computation → Parameterized complexity and exact algorithms
  • Propositional satisfiability SAT
  • Backdoors
  • Parameterized Algorithms


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