Rational index of bounded-oscillation languages

TL;DR

This paper studies the rational index of bounded-oscillation languages, showing it is polynomial, which impacts the complexity of related computational problems like CFL-reachability and Datalog query evaluation.

Contribution

It establishes that the rational index of bounded-oscillation languages is polynomial, providing upper bounds and extending understanding of their computational complexity.

Findings

Rational index of bounded-oscillation languages is polynomial.

Provides upper bounds for the rational index of these languages.

Implications for complexity of CFL-reachability and Datalog queries.

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.