Fine-grained reductions around CFL-reachability

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.