Abstract

Infinite subfamilies ℒ 1 , ℒ 2 ..., ℒ ∞ , ℒ ω of the family consisting of contextsensitive languages, are introduced such that ℒ 1 C ≠ ℒ 2 C ≠ ⋯C ≠ ℒ ∞ ℒ ω , where ℒ 1 is the family of ∈-free context-free languages, ℒ ω is the family of context-sensitive languages, and each ℒ n is an Abstract Family of Languages, i.e., closed under +, ·, U, inverse-homomorphism, ∈-free homomorphism, and intersection with regular sets. Each language of ℒ n is defined by a grammar, called a state grammar, that may be thought of as a context-free gramma with states.

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