Question

Consider the language L3 over alphabet Σ = { a, b }, L3 = { w ∈ Σ* | w is a palindrome of any length}.

Construct a PDA that recognizes L3.

Implement that PDA in JFLAP

Answer #1

For Automata class:
Let L be a regular language over the binary alphabet. Consider
the following language over the same alphabet: L' = {w | |w| = |u|
for some u ∈ L}. Prove that L' is regular.

Given an alphabet Σ = {a, b, c, d} Use Lecture definition to
construct a nondeterministic automaton M such that L = {w ∈ Σ ∗ :
at least one letter from Σ is missing in w}
1. (5pts) Draw the diagram Just draw the diagram, do not list
the components
2. (2pts) Explain shortly why your M is nondeterministic and why
it is correct
3. (3pts) Show that (s, accabb) `M ∗ (q, e) by constructing a
computation of...

Write a Turing-machine style of algorithm to decide the
language L1 given below. Use specific, precise, step-by-step
English. So, describe how to test whether or not an input string is
in the language L1 in finite time. No need to write a state
diagram.
L1 = {w : every ‘a’ within w is to the left of every ‘b’
within w} over the following alphabet
Σ = {a, b, c}. In other words, you’re not allowed to have any ‘b’...

Create an nfa for Σ = {a,b} that accepts the
complement of the language defined by the
following nfa:
states: {q0,q1}
input alphabet: {a,b}
initial state: q0
final states: {q1}
transitions:
δ(q0,b) = {q1}
δ(q0,λ) = {q1}
δ(q1,a) = {q0}

Use the pumping lemma to show that {w | w belongs to {a,
b}*,and w is a palindrome of even length.} is not
regular.

The Hermetian alphabet consists of only letters A, B, and C. A
word in this language is an arbitrary sequence of no more than four
letters. How many words does the Hermetian language contain?

Find a regular expression to describe:
The set of all strings over the alphabet {a, b, c, d}
that contain exactly one a and exactly one b
So, for example, the following strings are in this
language:
ab, ba, cccbad, acbd, cabddddd, ddbdddacccc
and the following strings are NOT in this
language:
a, ccbc, acbcaaacba, acacac, bcbbbbbca, aca, c, d,
b

Write a Turing-machine style of algorithm to decide the
language L2 given below. Use specific, precise, step-by-step
English. So, describe how to test whether or not an input string is
in the language L2 in finite time. No need to write a state
diagram.
L2 = {w : w has more a’s than it has b’s and c’s
combined} over the alphabet Σ = {a, b, c}.
Example strings: abaca ∈ L2. bcaa ∉ L2.

Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c occur consecutively and in that
order?
In how many of these permutations does a appear before
b and b appear before c?

Design a DFA accepting the language of all strings over Σ = {0,
1} with the property that the number of 0s and the number of 1s in
a string are both odd.

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