Sequential grammars and automata with valences

We discuss the model of valence grammars, a simple extension of context-free grammars. We show closure properties of context-free valence languages over arbitrary monoids. Chomsky and Greibach normal form theorems and an iteration lemma for context-free valence grammars over the groups Zk are proved. The generative power of different control monoids is investigated. In particular, we show that context-free valence grammars over finite monoids or commutative monoids have the same power as valence grammars over finite groups or commutative groups, respectively.

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