In s-grammar all productions are in form of
A → 𝑎𝛼 , A∈V , a∈T , 𝛼∈V*
"... and any pair (A, a) occurs at most once in P." [P. Linz, 6th ed. , p. 144]
s-grammar is Unambiguous and i think (not sure) we can describe all Unambiguous-CFL by s-grammar. I want to know can s-grammar describe all possible DCFL or not ? according to this sentence, I think we can't do it but i'm not sure about that:
Unfortunately, not all features of a typical programming language can be expressed by an s-grammar. [P. Linz, 6th ed. , p. 152]
but all languages which described by an s-grammar is Deterministic.
I say this, because we can made 2-state DPDA for any simple-grammar with this definition:
R ≝ Production Rules of CFG (x,y,"LBL") is a labeled-edge between x and y with “LBL” as a label ∀r∊R: r= (A,aⱰ) ( A∊V ⋀ a∊T ∧ Ɒ∊V*) add (q,q,"a,A/Ɒ") to E Add (q,q,"ε,z/Sz′") to E Add (q,f,"ε,z′/z′") to E
if there is any DCFL that we can not provide an s-grammar for it , show me that please and correct me if i'm wrong.