Some Sidenotes upon My Tentative Proof of Chomsky(1956)'s Claim concerning FSG.
The Claim : if S has an m -termed dependency set, then at least 2^m states are necessary for the FSG that generates L. Here is The proof . It's proven based on the Myhill-Nerode Theorem . I'm working on this simply because: It's a crucial point in understanding the whole motivation of the development of transformational grammar. Simply put, for a FSL contains m dependencies, the FSG that could generate it would need at least 2^m such states. In other words, a FSG with 2^m states could at most generate a FSL with m dependencies. More generally, for any finite state grammar, the language it generates shall contain finite number of dependencies. Natural language, however, has no such upper bound. It is for this reason that natural language could not be adequately described by the type of FSG defined in Chomsky(1956). My interactions with people in the field (of linguistics) informed me that there is systematic ignorance of the research...