Path of exact cost in edge labelled DAG?
Yes, it's NP-complete, by a reduction from subset sum. It's easiest to see using a multigraph: make a directed path, double each edge, and make one of the two doubled edges have cost zero, then cost $a$ can be achieved if and only if it is the sum of some subset of the weights of the nonzero edges. If you don't like multigraphs, subdivide the edges.

If you assume that $\max w_i&lt;C$ then there's a dynamic programming algorithm with time $O(mnC)$: just process the nodes in a topological ordering, and for each node calculate the set of path lengths by which it can be reached from $s$.