Satisfiability Algorithm for Syntactic Read-k-times Branching Programs

Atsuki Nagao, Kazuhisa Seto, Junichi Teruyama

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].