An iteration theorem for one-counter languages.
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Formal languages and their relation to automata
Formal languages and their relation to automata
Journal of Computer and System Sciences
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A solution is presented for the following problem: Determine a procedure that produces, for each full trio L of context-free languages (more generally, each trio of r.e. languages), a family of context-free (phrase structure) grammars which (a) defines L, (b) is simple enough for practical and theoretical purposes, and (c) in most cases is a subfamily of a well-known family of context-free (phrase structure) grammars for L if such a well-known family exists. (A full trio (trio) is defined to be a family of languages closed under homomorphism (&egr;-free homomorphism), inverse homomorphism, and intersection with regular sets.)The key notion in the paper is that of a grammar schema. With each grammar schema there is associated a family of interpretations. In turn, each interpretation of a grammar schema gives rise to a phrase structure grammar. Given a full trio (trio) L of context-free (r.e.) languages, one constructs a grammar schema whose interpretations (&egr;-limited interpretations) then give rise to the desired family of grammars for L.