Grammar-Based Construction of Indexes for Binary Jumbled Pattern Matching

We show how, given a straight-line program with g rules for a binary string B of length n, in O ( gn ) time we can build a (2nH0(B)+ o(n))-bit index such that, given m and c, in O(1) time we can determine whether there is a substring of B with length m containing exactly c copies of 1. If we use O(n log n) bits for the index, then we can list all such substrings using O(m) time per substring.