title: Design a PDA of all strings of 0's and 1's so that the number of 1's is twice the number of 0's
body: <p>While practicing for my final exams I found this question in <strong>Automata Theory, Language and Computation by J. Hopcroft, R. Motwani, J. Ullman</strong> on <strong>page 222</strong>.</p>
  
  <p>PDA should accept string in which the count of number of 1's is twice of number of 0's and if I'm not misinterpreting the question, the string can have different sequence of 0's and 1's in no particular pattern or specific order.</p>
  
  <p>My first approach to this problem was to divide the problem in two parts</p>
  
  <ol>
  <li>PDA for strings starting with 0. (For Example - 010111)</li>
  <li>PDA for strings starting with 1. (For Example - 110101)</li>
  </ol>
  
  <p>But dividing the problem don't seems to reduce the complexity of the problem.</p>
  
  <p>What should be ones approach to such problems?</p>