Question

Design a PDA to accept each of the following languages. You may use either PDAs that accept by final state or ones that accept by empty stack, whichever is more convenient.

a) The set of all binary strings with more 1's than 0's.
b) The language in Q1(a).
For each PDA, please show the transition diagram instead of a sequence of transitions.

Answer 1

The answer explains using the stack to track the difference in the number of 1's and 0's, with detailed guidance on constructing the transition diagram for the PDA.

Step-by-step explanation:

The subject of the question is the design of a Pushdown Automaton (PDA) to recognize specific languages—in this case, binary strings with more 1's than 0's. Designing such a PDA involves creating a transition diagram that accurately represents the operations of the automaton as it processes strings from the given language.

To accept the language of binary strings with more 1's than 0's, one approach is to use the stack of the PDA to track the difference between the number of 1's and 0's that have been read. For example, when a 1 is read, a symbol (such as 'X') could be pushed onto the stack, and when a 0 is read, a symbol is popped from the stack if the stack is not empty. If the input ends and the stack is not empty (meaning there are more 1's than 0's), the PDA will be in an accepting state.

For the transition diagram, we would create a starting state where the PDA stays if it reads a 1 and pushes 'X' onto the stack. If it reads a 0 and there are 'X's on the stack, it will pop an 'X' and stay in that state. If it reads a 0 and the stack is empty, it could transition to an error state to indicate that the string has been rejected. The accepting state(s) will be reached when the input is exhausted, and the stack is not empty.