Context-Free Grammars with Linked Nonterminals

We investigate a new type of finite copying parallel rewriting system, i.e., grammars with linked nonterminals, which extend the generative capacity of context-free grammars. They can be thought of as having sentential forms where some instances of a nonterminal may be linked. The context-free-like productions replace a nonterminal together with its connected instances. New links are only established between symbols of the derived subforms. A natural limitation is to bound the degree of synchronous rewriting. We present an infinite degree hierarchy of separated language families with the property that degree one characterizes the regular and degree two characterizes context-free languages. Furthermore, the hierarchy is a refinement of the known hierarchy of finite copying rewriting systems. Several closure properties known from equivalent systems are summarized.