We develop a set of new tabular parsing algorithms for Linear Indexed Grammars, including bottom-up algorithms and Earley-like algorithms with and without the valid prefix property, creating a continuum in which one algorithm can in turn be derived from another. The output of these algorithms is a shared forest in the form of a context-free grammar that encodes all possible derivations for a given input string.

In an information system indexing can be accomplished by creating a citation based on context-free parses, and matching becomes a natural mechanism to extract patterns. However, the language intended to represent the document can often only be approximately defined, and indices can become shared forests. Queries could also vary from indices and an approximate matching strategy becomes also necessary. We present a proposal intended to prove the applicability of tabulation techniques in this context.