Hi I have been having some trouble with a question now for some time, could somebody help me out, I have come up with the following but I don't believe it is correct.

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# Question

(b)

Give the specification of a finite state acceptor for the language L

over the alphabet {p, q, r, s} consisting of all non-empty finite strings involving the

letters p, q and r and s in which the letter p is always followed by the letter q and

the letter r is always followed by the letter s. ln particular, you should specify the

starting state, the finishing state or states, and the transition table for this finite

state acceptor.

----------------------------------------------------------------------------------------

is this correct ?

+----+++-------------------+

| -_ ||| P_ | Q_ | R_ | S_ |

|----|||----|-----|----|-----|

| S_ ||| T1 | T2 | T3 | T2 |

| T1 ||| E_ | T2 | E_ | E_ |

| T2 ||| T1 | T2 | T3 | T2 |

| T3 ||| E_ | E_ | E_ | T4 |

| T4 ||| T1 | F_ | T3 | F_ |

| F_ ||| E_ | E_ | E_ | E_ |

| E_ ||| E_ | E_ | E_ | E_ |

+----+++----+----+----+----+

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(c)

Devise a regular grammar for part (b)

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is this correct ?

<S> -> P<A> | Q<C>| R<B>| S<C>

<A> -> Q<C>

<B> -> S<C>

<C> -> P<A> | Q<C>| R<B>| S<C> | E

<F> -> E

Thanks