Abstract
This chapter introduces basic notions on families of languages. Rational cones are defined in Section 2, and closure properties of cones are derived from the examples of Chapter III. The second important type of families of languages considered in this book, namely full AFLs, is defined in Section 4. The next section contains basic facts about substitutions in relation with cones and full AFLs. In Section 6, we study the family of linear languages which is shown to be a principal cone, but not a full AFL. In the last section, we prove the incomparability of some special languages.
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