The complexity of computing maximal word functions

Eric Allender

Department of Computer Science
Rutgers University
New Brunswick
New Jerwey 08903, USA

Danilo Bruschi and Giovanni Pighizzini

Dipartimento di Scienze dell'Informazione
Università degli Studi di Milano
via Comelico 39 -- 20135 Milano, Italy
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. By the ``maximal word function'' of a language $L\subseteq\Sigma^*$, 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.