A new grammatical transformation into LL(k) form (Extended Abstract)

• Authors: Michael Hammer
• Venue: STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
• Year: 1974

For some time, it has been recognized that left-to-right deterministic top-down parsing has a number of features to recommend it. The logic of such a parser is easily expressed as a one-state pushdown machine, and very flexible translations can readily be performed in conjunction with top-down processing. The major difficulty with this style of parsing is that there are relatively few grammars which satisfy the rather restrictive requirements to admit of top-down parsing (the LL(k) grammars), in comparsion with grammars that can be parsed deterministically bottom-up (the LR(k) grammars). There has been some research along the lines of trying to apply transformations to non-LL(k) grammars in order to convert them into equivalent LL(k) form [1,2,3]; the most successful approach has been that of Rosenkrantz and Lewis [4]. They define class of grammars, the LC(k) grammars, which can be parsed in a mixed hybrid of top-down bottom-up techniques; this class strictly includes the LL(k) grammars, as well as many interesting but non-LL(k) grammars. They then provide a deterministic algorithm for converting any LC(k) grammar into an equivalent LL(k) grammar. This work is a generalization of, and in the same spirit as, the Lewis and Rosenkrantz program. We investigate a new hybrid parsing method, basically bottom-up in character, but which contains a minimal infusion of top-down ideas. We consider the class of grammars which can be parsed by this method, and observe that it strictly includes the class of LC(k) grammars. Then we exhibit an algorithm for deriving from any such grammar an equivalent LL(k) grammar; this derived grammar is also as “useful” as the original one in directing compilation activities, for it can support translations equivalent to those supportable by the original grammar.