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Satisfiability Algorithm for Syntactic Read-k-times Branching Programs

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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. In a preliminary version of this paper, we provide a satisfiability algorithm for syntactic read-k-times branching programs with n variables and m edges that runs in time \(O\left (\text {poly}(n, m^{k^{2}})\cdot 2^{(1-4^{-k-1})n}\right )\). In this paper, we improve the bounds for k = 2. More precisely, we show that the satisfiability of syntactic read-twice branching programs can be solved in time \(O\left (\text {poly}(n, m)\cdot 2^{5n/6}\right )\). Our algorithm is based on the decomposition technique shown by Borodin, Razborov and Smolensky [Computational Complexity, 1993].

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Authors and Affiliations

  1. Ochanomizu University, Tokyo, Japan

    Atsuki Nagao

  2. Seikei University, Tokyo, Japan

    Kazuhisa Seto

  3. University of Hyogo, Kobe, Japan

    Junichi Teruyama

Authors
  1. Atsuki Nagao
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  2. Kazuhisa Seto
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  3. Junichi Teruyama
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Correspondence to Junichi Teruyama.

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A preliminary version of this paper appeared in the Proceedings of the 28th International Symposium on Algorithms and Computation (ISAAC 2017). This work was supported in part by JSPS KAKENHI (18K11170, 18K18003) and JST CREST Grant Number JPMJCR1402, Japan.

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Nagao, A., Seto, K. & Teruyama, J. Satisfiability Algorithm for Syntactic Read-k-times Branching Programs. Theory Comput Syst 64, 1392–1407 (2020). https://doi.org/10.1007/s00224-020-09996-3

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