Input-driven languages are linear conjunctive

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 cont...

Automaton Representation of Linear Conjunctive Languages

Conjunctive languages are closed under inverse homomorphism

It is proved that the inverse homomorphic image of every language generated by a conjunctive grammar can be generated by a conjunctive grammar as well, and, given an arbitrary grammar G over an alphabet Γ and a homomorphism h : Σ∗ → Γ∗, a grammar for the language h−1(L(G)) ⊆ Σ∗ can be effectively constructed. Together with the known results on conjunctive grammars, this implies that the languag...

Generalizing input-driven languages: Theoretical and practical benefits

Regular languages (RL) are the simplest family in Chomsky’s hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of their related problems are decidable, so that they support automatic verification algorithms. Also, they can be recognized in real-time. Context-free languages...

Linear Context-Free Languages Are in NC

This paper concerns linear context-free languages (LIN). We prove that LIN ⊆ NC (under UE∗−uniformity reduction). We introduce a new normal form for context-free grammars, called Dyck normal form. Using this new normal form we prove that for each context-free language L there exist an integer K and a homomorphism φ such that L = φ(D′ K), where D′ K ⊆ DK , and DK is the one-sided Dyck language o...