Question

Construct a **deterministic** PDA for L = {w ∈ {a,
b}* : n_{a} (w) = n_{b} (w)}

Answer #1

Here we have 2 different paths to final state q3 since the starting symbol can be either a or b. Path from q0-q1-q3 is when starting symbol is a and path from q0-q2-q3 is when starting symbol is b.

In the q0-q1-q3 path, push all a's onto stack. And pop an 'a' when b occurs.

a, z|a -> Push a onto stack when stack is empty.

a, a|aa -> Push a onto stack when top element of stack is a.

Finally €, z|z means when we have reached to end of symbol and stack is empty, then go to state q3 which is final state. String which lead to state q3 are the string which are accepted by PDA

If you have any questions comment down. Please just don't simply downvote and leave. If you are satisfied with answer , please? upvote.. I really need it, thanks

Find a regular expression for the following language
L= {w∈{a,b}*:(na(w)-nb(w)mod)3=1}
please show explanation and steps

Question 2
a) Construct a Pushdown Automaton (PDA) for the language L (M) = {a, b}* where, if there
are any a’s must precede all b's and the number of b's must be equal to or twice the number
of a’s.
a) Trace the computations for the strings aabb, bbb, and abb in the PDA obtained in Question 2

PDA for L = {a^i b^j | i<j}
PDA for L = {a^i b^j | i>j}

Construct an NFA for the following language:
L = {w ∈ {a,b}∗ : every a is immediately followed by at most 2
b's}

Consider the language L = { w w : w ∈ { 0 , 1 } ∗ } is not
context-free. Note that this is the language of all strings that
consist of some combination of 0s and 1s, followed immediately by
that same combination of 0s and 1s. For example, 0101, 101101, and
110110 are all in the language because they consist of a string
followed by itself. Can you build a PDA to recognize this language?
(Hint: you...

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

Use CFG or PDA to prove L=
{0a1b0c : b ≠ a + c; a, b, c ≥ _0}
is a context-free language. Please add your explanation, thank
you.
If you can use the theorem(union of CFL and regular language =
CFL) is also welcomed.

Let two Einstein solids be in thermal contact with NA = NB = 2.
Assume that the resulting system is isolated and that it contains 9
units of energy (that is, UA + UB = 9ε).
(a) Construct a table with UA, UB, ΩA, ΩB, and ΩAB for all possible
macropartitions of the system.
(b) Calculate the probabilities of each of the possible
macropartitions.
(c) Identify the most likely macropartitions.

PDA for {a^i b^j i != j}
PDA for {a^i b^j c^k, i = j or j = k}
PDA for # of a's = # of b's
PDA for # b's = twice # of a's

1. If L={a^nb^n: n>=0} then what is the CFG of L* ?

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