Normal forms for phrase-structure grammars

Nonterminal complexity of one-sided random context grammars

“…Then, by Lemma 1, there is a phrasestructure grammar in the Geffert normal form Before proving that L(H ) = L(G), let us informally describe the meaning of rules introduced in (1)- (7). H simulates the derivations of G that satisfy the form described in Lemma 1.…”

“…Since n + 1 ≥ 1, this derivation can be expressed as S ⇒ n x ⇒ w ⇒ * z, for some x ∈ V + . Without any loss of generality, we may assume that x is of the form x = x 1 x 2 x 3 x 4 , where x 1 ∈ {A, AB} * , x 2 ∈ {S, ε}, x 3 ∈ {BC, C} * , and x 4 ∈ T * (see Lemma 1 and [7]). …”

“…G is in the Geffert normal form (see [7]) if it is of the form G = {S, A, B, C}, T, P ∪ {ABC → ε}, S , where P contains context-free rules of the following three forms: (i) S → uSa, (ii) S → uSv, and (iii) S → uv, where u ∈ {A, AB} * , v ∈ {BC, C} * , and a ∈ T .…”

“…Lemma 1 (see [7]) Let K be a recursively enumerable language. Then, there is a phrasestructure grammar in the Geffert normal form G such that L(G) = K .…”

Networks of Evolutionary Processors with Subregular Filters

“…A grammar G = (N, T, P, S) is in Geffert normal form ( [9]) if the set of nonterminals consists of the axiom S and three more letters A, B, C only and all rules in P have the form…”