Rational index of bounded-oscillation languages

Abstract

The rational index of a context-free language L is a function f (n), such that for each regular language R recognized by an automaton with n states, the intersection of L and R is either empty or contains a word shorter than f (n). It is known that the context-free language (CFL-)reachability problem and Datalog query evaluation for context-free languages (queries) with the polynomial rational index is in NC, while these problems is P-complete in the general case. We investigate the rational index of bounded-oscillation languages and show that it is of polynomial order. We obtain upper bounds on the values of the rational index for general bounded-oscillation languages and for some of its previously studied subclasses.