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Rational index of bounded-oscillation languages
The rational index of a context-free language is a function , such
that for each regular language recognized by an automaton with states,
the intersection of and is either empty or contains a word shorter than
. 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