# Tagged Questions

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### Gives regular expressions which defines regular language and what does {1,2} mean

The question is give a regular expression which defines a regular language. Question: The language over {0,1} consisting of all strings which either have length less than 3 or have 0 as their third ...
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### Finding a Regular Expression with a Specific Length from a language

Given this language, I was supposed to find the Regular Expression that represented it. Having given up and getting the answer later (below) I couldn't understand the regular expression. Given ...
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### Regular Expressions Help [duplicate]

I need a little help with Regular Expressions. The allowed operations are obviously + (union) , * (Kleene star) and concatenation. I have to write Regex for the following 2 examples. I have tried a ...
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### Formal Languages - Regular Expression

I've been battling the following two questions for more than a day today. Write a regular expression (comprised of {a, b}) that contain at least two b and do not contain abb. Write a regular ...
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### Minimal DFA for a given regular expression

How can I construct a minimal DFA from the following definition? $L=\{w \in \{a,b,c\}^*$: if the second-to-last letter from w is an $a$, then the number of $c$'s $\le 1\}$ I've already made a ...
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### Prove or disprove whether the following is a regular language

I'm given the regular language L, and w being an element of L. If we remove the w from the language L, will the resulting language be still regular? Well I thought to be true. Since initially is a ...
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### Checking some Regular Expression problems

I'm given the alphabet $$\Sigma = {\{a,b}\}$$ I tried to write a regular expressions for presenting the following sets: All strings in $$\Sigma ^ *$$ with: a-) number of 2s divisible by 4 b-) ...
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### Question about Notation in a Regular Language

I am a little confused about the following notation: $L' = \{xy|x\in L \ , y\in L^R\}$. I think this expression is not equivalent with palindrome but I am not entirely sure. For example, I think the ...
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### Prove by induction on a string

I want to practice proving the following: Given a binary string s, I want to prove $s$ has the same number of substrings 01 and 10 $\iff$ the first and last character of $s$ is the same. For ...
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### Construction of Regular Expression

I have the problem of needing to construct a regular expression corresponding to the set of strings of 0's and 1's whose number of 0's is divisible by five and whose number of 1's is even. ...
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### Proving that a regular expression belongs to a certain language

I've often come by questions that require proving that a certain regular expression belongs to that language. Example: Given $\Sigma = \{0,1\}$, and the language $L$ of all the words that have ...
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### Proving that $L= \{a^nb^n, n\ge 0\}$ is not a regular language.

The questions i'm 'stuck' on is: Let $\Sigma = \{0,1,2\}$ be the alphabet, and let $L$ be the collection of all the languages that contains only words that have even length. Prove that there are ...
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### Regular languages that are stutter-invariant but not star-free (LTL/FO-definable)

I am looking for simple examples and/or general ideas on regular languages (I am interested in finite words and infinite words alike) that are stutter-invariant (a language $L$ over an alphabet $A$ is ...
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### Is $\{w \in \Sigma ^* : |w|_2 mod 4 = 2\}$ a regular language?

Given alphabet $\Sigma = \{1,2,3\}$, is $\{w \in \Sigma^* : |w|_2 \bmod 4 = 2\}$ a regular language? I tried so hard on finding a regular expression but couldn't...
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### $L$ is a class of languages that cannot be represented by a regular expression. How to state cardinality of $L$.

$L$ is a class of languages that cannot be represented by a regular expression. The book says that the cardinality of $L$ is $2^{\aleph_0} > \aleph_0$ what's the logic behind getting the ...
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### Regarding regular expression. why do the following strings not exist in the expression.

Let L be the language defined by the regular expression: (a U b U c)((ab U ac U b)*(a U b) U (aa)*) the answer book says that 'aaaa' and 'aaaaaa' do not belong to L. I can show that aaaa and aaaaaa ...
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### set of all reg exp vs set of all languages

$\Sigma$ = {a,b,c,d,e} V = {A,B,C,D,E,F,G,H} According to the notes: The set of all regular expressions over $\Sigma$ is infinite and countable. The set of all languages over $\Sigma$ is infinite ...
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### Give a regular grammar for L

Give a regular grammar for L= {a^n b^n : n<=100} I would do something like this : S---> A | empty string A---> aB| empty String B---> Ab but How do we keep count of the number in the grammar? ...
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### Is this proof using the pumping lemma correct?

I have this proof and it goes like this: We have a language $L = \{\text{w element of } \{0,1\}^* \mid w = (00)^n1^m \text{ for } n > m \}$. Then, the following proof is given: There is a $p$ ...
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### Regular languages question

Describe these languages over $\Sigma={a,b}$ $\Sigma^{*}(a\cup\epsilon)b^*$ $a\Sigma\Sigma^*b\Sigma\cup b\Sigma\Sigma^{*}a\Sigma$ Just making sure I understand some basic concepts... First one ...
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### Basic regular expressions problem

I'm in an intro to CS theory class learning about regular expressions. I was wondering if people could give me hints as to whether I'm on the right track for these problems. I hope this particular ...
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### What are the states of this NFA?

I have to realize an NFA that recognizes the language of strings on the alphabet {a, b} ending with: bb, ba, baa. I thought that there must be the following states: $q_0$: the string ends with bb. ...
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### Proving or disproving regularity of a language

The question is as follows: If L1 and L2 are not regular and L1 ⊆ L ⊆ L2, then L is regular My intuition says that it's wrong so I've been looking for a ...
I'm stuck on these practice problems. If someone could help me solve them it would be great. What is a contextfree grammar for the langauge $L = \{a^i b^j c^j d^i \mid i,j \ge 0\}$ The following ...