Grammars with Minimal/Maximal Use of Selectors

Abstract

Let us now systematically examine the possibility of generating the languages L ₁,L ₂, L ₃ below with grammars of the types considered up to now:

$$ {L_1} = \left\{ {{a^n}{b^n}{c^n}\left| {n \geqslant 1} \right.} \right\}, $$

,

$${L_2} = \left\{ {xcx\left| {x \in {{\left\{ {a,b} \right\}}^*}} \right.} \right\}, $$

,

$${L_3} = \left\{ {{a^n}{b^m}{c^n}{d^m}\left| {n,m \geqslant 1} \right.} \right\}, $$

.