Backus' language

l)ear Editor: [ h a v c read Dr. Saul Gorn's recent article, "Specification L:mguages, etc." in the Comm,~nicatio~s of the .-lC31 with interest, primarily t)eeause [ have been doing a bit of research in my spare time considering various im/)lications of "Backus nornlal form." I was surl)rised to see the Backus notation listed as bring mechanically translatat)le into "regular exl)ressions'" or trees, for [ believe this is not possible and I will "provC' this statement below. I also question the value of an "infinite" alphabet in Backus notation, because there are only a finite number of productions and a finite number of characters in each production, so how can we use more than a finite alphat)et? Perhaps, I misunderstand the statements. An interesting language which I believe is equivalent to Backus' language was develot)ed at Case Tech last summer. It is a reeursive type of state diagram, where the symbols on the ':tape" are either alphabetic letters or the names of a whole new st:ate diagram. In the latter ease the diagram has only one output :.rod one input and the meaning is "if we can get from the inlmt to the outl)ut we have essentially been able to read this construct from the tape." For example, we can describe the possibh~ expressions of your prefix language by