The complexity of computing maximal word functions

Maximal word functions occur in data retrieval applications and have connections with ranking problems, which in turn were first investigated in relation to data compression [21]. By the "maximal word function" of a language L {subset double equals} ∑^*, we mean the problem of finding, on input x, the lexicographically largest word belonging to L that is smaller than or equal to x. In this paper we present a parallel algorithm for computing maximal word functions for languages recognized by one-way nondeterministic auxiliary pushdown automata (and hence for the class of context-free languages). This paper is a continuation of a stream of research focusing on the problem of identifying properties others than membership which are easily computable for certain classes of languages. For a survey, see [24].