title: Proving Equivalence of TM and DFA
body: <p>I'm trying to prove that TM = DFA is undecidable using reduction from Halting Problem
  Theoretically I understand that Turing Machine captures all the computable functions and DFA only capture the functions that can be computed in constant space therefore TM = DFA is undecidable.</p>
  
  <p>Here are my steps:
  Suppose that R that decide L(M)=L(D)</p>
  
  <p><strong>EQ_DM = { [D,M] | L(M) = L(D) }</strong> <br/><br/>
  and we create a turing machine </p>
  
  <p><strong>HALT_TM = { [M,w]  |  (M halt on input w→Accept <br/>
                  M did not halt on input w→Reject)}</strong></p>
  
  <p>How do I construct a D &amp; M so R[D,M] tells if M halt on w?</p>