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Satisfiability Algorithm for Syntactic Read-$k$-times Branching Programs

Authors Atsuki Nagao, Kazuhisa Seto, Junichi Teruyama

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Atsuki Nagao
Kazuhisa Seto
Junichi Teruyama

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Atsuki Nagao, Kazuhisa Seto, and Junichi Teruyama. Satisfiability Algorithm for Syntactic Read-$k$-times Branching Programs. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 58:1-58:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ISAAC.2017.58

Abstract

The satisfiability of a given branching program is to determine whether there exists a consistent path from the root to 1-sink.
In a syntactic read-k-times branching program, each variable appears at most k times in any path from the root to a sink.
We provide a satisfiability algorithm for syntactic read-k-times branching programs with n variables and m edges that runs in time O\left(\poly(n, m^{k^2})\cdot 2^{(1-\mu(k))n}\right), where \mu(k) = \frac{1}{4^{k+1}}. Our algorithm is based on the decomposition technique shown by Borodin, Razborov and Smolensky [Computational Complexity, 1993].

Subject Classification

Keywords
  • branching program
  • read-k-times
  • satisfiability
  • moderately exponential time
  • polynomial space

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