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arXiv · 2012.03567

Rational index of bounded-oscillation languages

Ekaterina Shemetova·Alexander Okhotin·Semyon Grigorev
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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.

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Ekaterina Shemetova, Alexander Okhotin, Semyon Grigorev. 2020-12-07. Rational index of bounded-oscillation languages. https://arxiv.org/abs/2012.03567

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