  In this paper we study the fine-grained complexity of the CFL reachability
problem. We first present one of the existing algorithms for the problem and an
overview of conditional lower bounds based on widely believed hypotheses. We
then use the existing reduction techniques to obtain new conditional lower
bounds on CFL reachability and related problems. We also devise a faster
algorithm for the problem in case of bounded path lengths and a technique that
may be useful in finding new conditional lower bounds.
