# create two- or three-tape Turing machine to recognize the language $0^{2^n}$

I am creating a two-tape Turing machine to recognize the language $$\{0^{2^n}|n\geq 0\}$$. My idea is to put an input string, such as 0000, at the first tape, and use the second one to count the number of 0s in binary form (as a suggestion at A two-tape deterministic Turing machine that recognizes an exponential string). Every time Turing machine read a single 0, increase the counter (on the second tape) by 1. My difficulty is to write clearly the transition function, namely $$\delta$$, such as, I don't know how many states this Turing machine should have.

• Are you supposed to give $\delta$ and the TM states explicitly? Usually, a precise description (in prose) suffices. – dkaeae Dec 30 '18 at 13:23
• Well, you decide how many states the machine needs. Enough states to remember what it is supposed to be doing. – Hendrik Jan Dec 30 '18 at 15:04