[answered] Book reference :Introduction to computer theory 1) Convert

Can someone please help me with the questions in the file attached from Finite Automata theory? Thanks

Book reference

:Introduction to

computer theory 1) Convert the following FA into a PDA. 3) Eliminate L-productions for the CFG:

S ? aXbX

X ? aY | bY | L

Y ? X | ZY | b

Z ? XY | c

4) Convert the following CFG into CNF.

S ? ABC

A ? aAS | a | L

B ? SbS | A | bb

C?b 2) Convert the following FA into a CFG. 5) Consider the following non-deterministic PDA. Are the following words accepted by this

PDA? For those that are rejected, indicate which state the PDA is in when the crash occurs.

(a) aaabbb

(b) bbbaaa

(c) aaabbaa

(d) aaaabaa

(e) aaabaa 6) Use the algorithmic approach (Chapter 17 from the textbook or Topic 15 from the lecture

notes) to create a CFG for the language L = b(a*b+a)*

7) Consider the following Turing Machine: Show the execution traces using each of the following

input strings:

(a) aaa

(b) aba

(c) ababb

(d) What does the machine do? 8) Build a Turing Machine over the alphabet G = {a,b} that accepts all words which start and end

with the same letter. Note that this is a Regular Language. Show the execution traces with the

following input strings:

(a) baa

(b) aba

(c) b 9) Build a TM over the alphabet E={a, b} that accepts the language DoubleA where each word

has twice as many a?s as b?s. You might find it easier if you use the Insert# routine.

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