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Satisfiability Algorithm for Syntactic Read--times Branching Programs
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 Oleft(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]