While natural language is usually analyzed from left to right, bidirec
tional parsing is very attractive for both theoretical and practical r
easons. In this paper, we describe a formal framework for bidirectiona
l tabular parsing of general context-free languages, and some applicat
ions to natural language processing are studied. The framework is gene
ral and permits a comparison between known approaches and the algorith
ms outlined here. A detailed analysis of the redundancy problem is giv
en and a technique for improving the performance of bidirectional tabu
lar parsers, whilst maintaining the flexibility of bidirectional strat
egies, is described. An algorithm for head-driven parsing and a genera
l algorithm for island-driven parsing are studied. The former allows a
nalyses of each constituent to be triggered by some fixed immediately
dominated element, chosen on the basis of its information content. The
latter permits analyses to start from any dynamically chosen position
s within the input sentence, combining bottom-up and top-down processi
ng without redundancy.