# regular-languages's questions - English 1answer

1.001 regular-languages questions.

### 2 Closure of regular languages under deleting a 1 from each even run of 1s

Let $R$ be a regular set over the alphabet $\{0, 1\}$. Give a machine construction to prove that the set obtained by deleting one 1 from each even length block of 1’s is also regular, and using ...

### 1 Proving irregularity of $\{a^nb^k \mid n > k \text{ or } n \neq k-1\}$

1 answers, 6 views regular-languages pumping-lemma
I need help with proving the following language is not regular: $$L = \{ a^n b^k \mid n > k \} \cup \{ a^n b^k \mid n \neq k-1 \}$$ My usual methods using pumping lemma are not getting me ...

### 2 Regular expression for words over $\{0,1\}$ containing at least one 1

I had an exam on Theory of Computation, and one of the questions was to write down a regular expression for the language over $\{0,1\}$ consisting of all words containing at least one 1. My answer was:...

### 17 Regular expressions with backreferences over unary alphabet

Setting: regular expressions with backreferences unary language (1-symbol alphabet) Is the following problem decidable in this setting: Given a regular expression with backreferences, does it ...

### 2 Is DFA and Regular Expression equivalent?

The language of a DFA can be the empty set (by defining no final states), but can a Regular Expression do that? If Regular Expression cannot do that, does it mean that DFA and Regular Expression are ...

### 6 How to prove using pumping lemma that language generated by a(b*)c(d*)e is regular?

I am studying pumping lemma from Introduction to theory of computation by Michael Sipser. I wanted to check if the language generated by regular expression ...

### 1 Minimum number of letters

I have an assignment that I have to do and the question is Draw a DPDA that accepts the language L = {ba(bb)^(n+1)a^(n – 1) |n > 1}. Im not looking for the answer but rather some direction. I ...

### 11 Star free language vs. regular language

I was wondering, since $a^*$ is itself a star-free language, is there a regular language that is not a star-free language? Could you give an example? (from wikipdia) Lawson defines star-free ...

### 4 Is the symmetric difference of a non regular language L and a finite language f non regular?

The symmetric difference of $L_1$ and $L_2$ is defined to be: $(L_1-L_2) \cup (L_2-L_1)$. Problem: I’m trying to prove that given L a non regular language and F a finite language there symmetric ...

### -1 Prove {0^n OR 1^2n OR 2^3n | n >= 0} is not context free

How to prove using pumping lemma {0^n OR 1^2n OR 2^3n | n >= 0} is not context free This isnt the same language as {0^n1^2n2^3n | n >= 0} as this language the numbers need to be in order.

### 1 Proof that (A ∪ B)∘C = A∘C ∪ B∘C where A, B and C are languages

1 answers, 43 views formal-languages regular-languages
How can I prove this identity of languages? My aproach is the following: Let A, B and C to be languages, and let x to be an arbitrary string. (A ∪ B) ⇒ x ∈ A ∨ x ∈ B How do you proceed?

### Define a grammar to emmulate chess rules

Is it possible to define a 《chess language》: language={alphabet = {(chess pieces, squares of chess board)}, grammar={rules of movement of pieces over the board}}? I looked online but I cannot find a ...

### 1 Contradiction in regularity of a language

1 answers, 30 views formal-languages regular-languages

### 3 Complexity of CFG grammar for a regular language

I know that each regular language can be generated by a CFG. This makes, in one sense at least: context-free languages more general than regular languages. Are there known results about the '...