Changing Partitions in Rectangle Decision Lists

Author Stefan Mengel

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Stefan Mengel
  • Univ. Artois, CNRS, Centre de Recherche en Informatique de Lens (CRIL), Lens, France


The author would like to thank the reviewers for their generous and very detailed comments that greatly improved the presentation of this paper.

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Stefan Mengel. Changing Partitions in Rectangle Decision Lists. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Rectangle decision lists are a form of decision lists that were recently shown to have applications in the proof complexity of certain OBDD-based QBF-solvers. We consider a version of rectangle decision lists with changing partitions, which corresponds to QBF-solvers that may change the variable order of the OBDDs they produce. We show that even allowing one single partition change generally leads to exponentially more succinct decision lists. More generally, we show that there is a succinctness hierarchy: for every k ∈ ℕ, when going from k partition changes to k+1, there are functions that can be represented exponentially more succinctly. As an application, we show a similar hierarchy for OBDD-based QBF-solvers.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Proof complexity
  • rectangle decision lists
  • QBF proof complexity
  • OBDD


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