An Application of Mehlhorn's Algorithm for Bracket Languages to log(n) Space Recognition of Input-Driven Languages

The class of input-driven languages (idl's, for short) is presently the most complicated subclass of context-free languages known to be recognizable in the deterministic log(n) space. The idl's are a generalization of bracket languages; the strings of a bracket language contain an explicit information about the parse tree, while the strings of an idl contain an information about the behaviour of the pushdown store. Therefore, one could expect that there is a log(n) space recognizer of idl's which is a natural generalization of the corresponding recognizer of bracket languages. However, the algorithm presented in 1983 by Braunmiahl and Verbeek [2] for log(n) space recognition of idl's uses ideas quite different from those of the algorithm presented in 1976 by Mehlhorn [3] for log(n) space recognition of bracket languages. In this paper we show how a log(n) space recognizer for idl's can be derived in a natural way from Mehlhorn's algorithm. This is an exercise in the efficient elimination of recursion.