Question

**Show that language B = {〈A〉| A is a DFA and L(A) = Σ* }
is decidable.**

Answer #1

Show that language C = { <D, R> | D is a DFA, R is
a regular expression and L(D) = L(R)} is decidable.

a. Draw a DFA for the language of all strings over Σ = {?, ?}
that do not have two consecutive ?’s.
b. Define the transition function, ?, for the DFA in the
previous question.

Given a language L, etc.
Show that the language L is a regular language.
To show that the language L is a regular language - find/design a
dfa that recognizes the language L.
Given a regular expression r, etc.
What is the language L, L = L(r)?
L(r) is the set of all strings etc.

Let Σ = {a}, and let L be the language
L={an :nisamultipleof3butnisNOTamultipleof5}.
Is L a regular language? HINT: Maybe instead of an explicit DFA
or regular expression, you can find another argument.

Let L ⊆ Σ* be a regular language. Suppose a ∈ Σ and
define L\a = {x : ax ∈ L }. Show that L\a is regular.

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.

Show that every infinite semi-decidable language A has an
infinite subset B⊆A such that B is a decidable language.

1.1). The alphabet is {a, b}. Give the state diagram of the DFA
recognizing the language: {w | w has an odd number of a’s and at
least two b's}. Show the steps!
1.2). Give the state diagram of the DFA which recognizes the
complement of the above language in 1.1.
Use 1.1 to answer 1.2
**I ONLY NEED HELP WITH 1.2* PLEASE*

Let L be any non-empty language over an alphabet Σ. Show that
L^2⊆L^3 if and only if λ∈L.

Let S = {<M> | M is a DFA that accepts wR whenever it
accepts w}. Show that S is decidable. Let S = {<M> | M is a
DFA that accepts wR whenever it accepts w}. Show that S is
decidable.

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