Category "turing-machines"

Turing machine for multiplication of two unary number

I am creating a Turing machine that computes the multiplication of two numbers using unary representation within 300 step limit. For example 2 * 3 as 110111 and

Context-sensitive Grammar for a^nb^nc^n

Is the following CSG for a^nb^nc^n correct? S->aSbC|abc Cb->bC C->c If not please explain why?