 
Summary: THE COMPLEXITY OF COMPUTING
MAXIMAL WORD FUNCTIONS
Eric Allender, Danilo Bruschi
and Giovanni Pighizzini
Abstract. Maximal word functions occur in data retrieval applications
and have connections with ranking problems, which in turn were rst
investigated in relation to data compression 21 . By the maximalword
function" of a language L , we mean the problem of nding, 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 .
Subject classi cations. 68Q15,68Q25,68Q45.
1. Introduction
The traditional focus of complexity theory has been on the complexity of deci
