Simple Matrix Grammars and Their Leftmost Variants

In essence, simple matrix grammars can be seen as sequences of context-free grammars, referred to as their components, which work in parallel. The present paper demonstrates that two-component simple matrix grammars are as powerful as ordinary matrix grammars. Then, it places three leftmost derivation restrictions upon these grammars and demonstrates that under two of these restrictions, simple matrix grammars are computational complete--that is, they are equivalent with Turing machines. From a historical perspective, concerning simple matrix grammars, the paper also makes several remarks that correct false statements published about them in the past.