Your Question:

For each of the following languages, construct a grammar that recognizes it.

a){w∈{a,b}∗∣w has b 's followed by a′s}

Step By Step Answers with Explanation

1. First, let's create non-terminal symbols to represent different parts of the strings in the language.

- S: The start symbol

- B → ε | bB

- A → ε | aA

Now, let's consider some examples to see how this CFG works:

1. For the string "ba":

2. For the string "baaa":

- S derives B A

- S derives B A

- B derives bbbb

- B derives b

- A derives ε

- A derives aaaa

- The string "bbbaaaaaba" is invalid because it has 'b's followed by 'a's, but then it has another 'b' after 'a's.

- The string "bbbbaabababa" is valid because it allows for no 'a's after 'b's.

In summary, the CFG we have constructed generates strings that have 'b's followed by 'a's, including cases where there are no 'b's or 'a's. It correctly recognizes the language described.