0
$\begingroup$

Given a Turing Machine $$M = (\{q_0, q_1\}, \{0, 1\}, \{0, 1, B\}, δ, B, \{q_1\})$$ Where $δ$ is a transition function defined as $$δ (q_0, 0) = (q_0, 0, R)$$ $$δ (q_0, B) = (q_1, B, R)$$ The language $L(M)$ accepted by Turing machine is given as :

  1. $0^*1^* $
  2. $ 00^*$
  3. $10^* $
  4. $1^*0^*$

My attempt:

We, can draw DFA for given transition function of Turing Machine, and expression should be as $0^*$, but official key is given option $(2)\space 00^*$.

Can you explain it, please?

  • 2
    Yes, this TM is a DFA and recognizes $0^*$. – 2017-01-05
  • 0
    @FabioSomenzi, $00^*$ is subset of $0^*$, so, this TM can also accept the language $00^*$. Am I right? – 2017-01-05
  • 2
    Yes, $00^*$ is a subset of $0^*$, but normally one talks about *the* language accepted by a TM. One would, however, say that the TM accepts all the strings in $00^*$. – 2017-01-05
  • 0
    @FabioSomenzi, I did self-answer for this post, but, someone voted down my this answer without a comment. What is bad with this answer? – 2017-01-07
  • 0
    I don't know what prompted the down-vote (it's not mine). You may want to change "sting" into "strings" and replace $\in$ by $\epsilon$, tough. – 2017-01-07

1 Answers 1

-1

$00^∗$ is subset of $0^∗$, so, this TM can also accept the all string of $00^∗$. However other than $00^∗$ only $ϵ$ is also accepted by given TM.