Question

Give context-free grammars and draw state diagrams of PDAs that generate the following languages (Σ = {a, b}):

1) The set of strings over the alphabet {a, b} with more a’s than b’s (Σ = {a, b})

Answer 1

To generate a context-free grammar and a state diagram of a PDA that generates the language of strings with more a's than b's, follow these steps.

Step-by-step explanation:

In order to generate a context-free grammar and a state diagram of a pushdown automaton (PDA) that generates the language of strings over the alphabet {a, b} with more a's than b's, we can follow these steps:

1. Create a context-free grammar with a nonterminal symbol S as the start symbol. The production rules should generate strings with more a's than b's.
2. Construct a PDA based on the produced grammar. Each state in the PDA corresponds to a nonterminal symbol in the grammar, and the transitions are based on the production rules of the grammar.
3. Draw the state diagram of the PDA, where each state represents a nonterminal symbol and the transitions represent the possible productions.

Here's an example of a context-free grammar and a state diagram:

Grammar:
S → aSb | aS | ε

State Diagram:
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