On an equivalence of system-theoretical and categorical concepts
This paper discusses context-free rewriting systems in which there exist two disjoint finite sets of rules, and a symbol, referred to as a condition of applicability, is attached to each rule in either of these two sets. In one set, a rule with a symbol attached to it is applicable if the attached symbol occurs in the current rewritten string while in the other set, such a rule is applicable if the attached symbol does not occur there. The present paper demonstrates that these rewriting systems...
We introduce the notion of a differentiation function of a context-free grammar which gives the number of terminal words that can be derived in a certain number of steps. A grammar is called narrow (or -narrow) iff its differentiation function is bounded by a constant (by ). We present the basic properties of differentiation functions, especially we relate them to structure function of context-free languages and narrow grammars to slender languages. We discuss the decidability of the equivalence...
We introduce the notion of a differentiation function of a context-free grammar which gives the number of terminal words that can be derived in a certain number of steps. A grammar is called narrow (or k-narrow) iff its differentiation function is bounded by a constant (by k). We present the basic properties of differentiation functions, especially we relate them to structure function of context-free languages and narrow grammars to slender languages. We discuss the decidability of ...