Input-driven languages are linear conjunctive

Linear conjunctive grammars define the same family of languages as one-way real-time cellular automata (A. Okhotin, “On the equivalence of linear conjunctive grammars to trellis automata”, RAIRO ITA, 2004), and this family is known to be incomparable with the context-free languages (V. Terrier, “On real-time one-way cellular array”, Theoret. Comput. Sci.  , 1995). This paper demonstrates the containment of the languages accepted by input-driven pushdown automata (a.k.a. visibly pushdown automata) in the family of linear conjunctive languages, which is established by a direct simulation of an input-driven automaton by a one-way real-time cellular automaton. On the other hand, it is shown that the language families defined by the unambiguous grammars, the LR(k)LR(k) grammars and the LL(k)LL(k) grammars are incomparable with the linear conjunctive languages.