1. A method comprising, by a computing device: receiving, from a client device of a first user, a text string comprising one or more characters inputted by the first user; generating a set of suggested queries based on the text string, each suggested query in the set being based on a string generated by a grammar of a grammar model and comprising the text string of the query and one or more tokens inserted by the grammar model corresponding to one or more terms, respectively; calculating, for each suggested query in the set, a quality score based on an insertion cost of the one or more tokens of the suggested query inserted by the grammar model; filtering the set to remove one or more suggested queries from the set based on the respective quality scores of the suggested queries; and sending, to the client device, one or more of the suggested queries from the post-filtered set for presentation to the first user.