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1answer
33 views

Is $L_1$ context free language?

Let $L = L_1 \cap L_2 $, where $L_1$ and $L_2$ are languages as defined below: $L_1= \left \{ a^m b^mca^nb^m \mid m,n \geq 0 \right \}$ $L_2=\left \{ a^i b^j c^k \mid i,j,k \geq 0 \right \}$ Then L ...
1
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3answers
41 views

Find a regular expression for the following language

I was given an example in class. It goes as follows: Let the alphabet be $\{a, b\}$. $L$ is the string with one $b$ and at least two $a$'s Find a regular expression that generates this language. ...
0
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3answers
62 views

What is the difference between regular expression $(x + y)^*$ and $(x^*y^*)$? [closed]

What is the difference between regular expression $(x + y)^*$ and $(x^*y^*)$ ?
0
votes
1answer
55 views

Drawing automata for languages

I'm trying to draw two automata for these two languages: For the first one, I know that the minimum is n = 1, m = 1, but I'm having troubles drawing a NFA for it. The second one the minimum is n = ...
0
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0answers
18 views

Converting regular expressions to NFAs

I'm having trouble converting these regular expressions to NFAs For 1, does the plus sign mean I should draw each term individually and then make an epsilon state between them? Would this be ...
0
votes
1answer
23 views

regular expressions, notation w|w and w|?

I'm trying to give regular expressions for the following languages {a, b} What does w| and w|w mean? For the first question, I have (b(a+b))*, but I'm lost on the second.
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2answers
60 views

regular expressions $(a+b)^*$

If I have a regular expression $(a+b)^*$, does that mean I can't have the string $abba$ because the expression ends with a $b$? Or does this expression accept every string in the alphabet $\{a, b\}$?
2
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2answers
32 views

How to prove that $R_1(R_2R_1)^* = (R_1R_2)^*R_1$; Theory of computation

I need a formal proof for this property (or hints): Let $R_1$ and $R_2$ be to regular expressions : $R_1(R_2 R_1)^* = (R_1 R_2)^*R_1$ I don't know if the way I'm solving the problem is totally fine, ...
4
votes
1answer
62 views

Proving that all equivalent regular expressions are reachable via algebraic laws

Given a set of laws for regular expressions, for example (ripped from this document): $$ \begin{array}{llll} \text{1.} & (A|B)|C = A|(B|C) &\qquad& \text{(associativity of choice)}\\ ...
0
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0answers
18 views

How to formulate the following statement:

How to formulate the following statement: "If 1/3 of those who made it to goal instead had quit and 1/2 of those who had quit had made it to goal, the numbers of those who made it to goal would be the ...
0
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0answers
24 views

How to solve the following relationship?

We can easily seen that $${q^{2n}} = {q^n}\left( {{q^n} - 1} \right) + {q^n},{q^{3n}} = {q^n}{\left( {{q^n} - 1} \right)^2} + 2{q^n}\left( {{q^n} - 1} \right) + {q^n}.$$ Similarly, we assume that ...
0
votes
1answer
95 views

Writing regular expressions

So here's the problem: Let $Σ =\{a, b, c\}$. Write a regular expression for the set of all strings in $Σ^∗$ such that the sum of the number of $a$’s and $b$’s in the string is at most two. Thus the ...
0
votes
1answer
119 views

Give some examples of strings in, and not in, these sets, where Σ = {a,b}

Here's the set: {w : for some u ∈ Σ*, www = uu} From what I understand, it's saying "w (which is a string) such that for some u (which is another string) is an element of the possible combinations ...
1
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0answers
71 views

Rewriting regular expressions

For the following two regular expressions, how would I rewrite them as a simpler expression representing the same set? $b^* \cup a^* \cup (a \cup b)^*$ $\Big((a^*b^*)^*(b^* \cup a^*)^*\Big)^*$ I ...
2
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1answer
40 views

examples of “interesting” star-free languages

Can you point me to some examples (preferably known ones from the literature, but this is not crucial) of "interesting" / non-trivial star-free languages? I'm trying to get some intuitive sense of ...
-1
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2answers
58 views

Prove that $R_1 \times R_2$ is a regular language for $R_1, R_2$ regular [closed]

Let A and B be two sets. The cross products of A and B are defined as : AxB={(a,b): a belongs to A and b belongs to B }. Assume R1 and R2 are regular languages over an input alphabet Σ={a,b}. Prove ...
1
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1answer
26 views

Creating a regex expression for a regular language

$\{x \in \{0, 1 \} : x = 0^m1^n \hspace{.1cm} \text{for some} \hspace{.1cm} m, n \in N \hspace{.1cm} \text{such that} \hspace{.1cm} m * n \ge 3\}$. I've been stuck on trying to create a regex for ...
1
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1answer
21 views

Using induction to prova a regular expression belongs to the language generated by a grammar (well half-proving anyways)

I have a grammar with this productions S->aBSBBa |$ \epsilon $ B->bB|$\epsilon$ $L(B)=b^*$ (by Arden's rule) and seems that $L(S) = a(b+ab^*a)^*a + \epsilon$ I have to prove that last ...
1
vote
1answer
60 views

Arden rule proof

I'm studying Arden's Rule for regular languages, but I'm having troubles with the proof. Arden's rule states that the set A*⋅B is the smallest language that is a solution for X in the linear equation ...
1
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1answer
27 views

Is Σ* the same as saying L*

I'm getting confused over the two. Are they the same? The complement of a language L is Σ* - L. Is saying L* - L wrong?
0
votes
1answer
23 views

Proving that a language with a regular expression is context-free

If L = {ww : w ∈ L(1*01*)} it means that w = $1^a$0$1^b$ and ww = $1^a$0$1^b$$1^a$0$1^b$ If I want to prove that this language is context-free by giving a context-free grammar, can I give a CF ...
0
votes
1answer
32 views

Regular expression

I'm trying to find Strings of length 4 In this regular expression. However, I'm having trouble understanding how the string is built $$1(1+00)^*0+(01)^*+(101+0)(10+λ)1^*$$ For example, for ...
1
vote
1answer
58 views

Find regular expression that defines a given language

I want to find a regular expression that defines a language L over the alphabet {0,1} with a following condition: every word contains exactly two 000 substrings. For example, a valid word would be ...
0
votes
1answer
255 views

How would I draw a state transition diagram to satisfy this regular expression?

I somewhat understand finite state machines in concept however am unsure how I would apply it in this example. The question is Draw the transition diagram of a finite state recogniser which accepts ...
0
votes
1answer
42 views

Regular Expressions that define given languages

A few of these here I just wanted to make sure I had right. For $\Sigma = \{0,1\}$ a. The language consisting of all strings of 0's and 1's that have even length and where 0's and 1's alternate I ...
2
votes
3answers
72 views

The number of elements in a set

I have a small task, part of my homework, which tends to confuse me because of its simplicity. It makes me think that I am missing something. I have to find the number of elements in the set {w | w ∈ ...
2
votes
1answer
28 views

Finding regular expressions for which a given Turing machine halts and accepts, halts and rejects, and diverges.

Consider the Turing machine M = (Q,Σ,Γ,δ,q,F) F = {t} Q = {q,r,s,t,v,x} Σ = {a,b,c} Γ = {B,a,b,c} δ = [q,a,q,a,R] [q,b,q,b,R] [q,c,v,b,R] [q,B,r,B,L] [r,a,s,B,L] [r,b,s,B,L] [r,c,s,B,L] ...
0
votes
2answers
275 views

Describe as a regular expression the set of strings over {a,b,c} that contain the substrings aa,bb,cc

What would be an appropriate regular expression for this set of strings listed in my title? i have this so far: (aa,bb,cc) is a subset of all the strings listed (a,b,c) (it corresponds to the strings ...
0
votes
1answer
29 views

Constructing regular expressions for languages

I'm new to regular expressions and I'm currently working on some exercises to get familiar in constructing regular expressions for languages. I have the following languages, for which I already tried ...
0
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2answers
28 views

Languages and their Regular Expressions - Automata

I am working on some Automata practice problems. I am working a 2 part question. Here it is: Let $\Sigma = \{a,b\}$ be an alphabet. Let $L = \left\{w \in \Sigma^* \mid n_a(w) \le 4\right\}$ ...
0
votes
1answer
26 views

What is $h^{-1}(L)$, for $L$ a regular language and $h$ a homomorphism?

Let $L = L((00 + 1)^∗)$ and $h : \{a, b\}^* \to \{0, 1\}^*$ be defined by $h(a) = 01$ and $h(b) = 10$. What is $h^{−1}(L)$? In this context "$+$" means "$\cup$". So the language $L$ is all the ...
2
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2answers
60 views

A Regular Expression for all strings that…

I got a problem I have to solve, the problem says that given an alphabet $\Sigma = \{a, b, c\}$ I have to build a regular expression that describes the string with: An even number of a's. A 4k + 1 ...
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0answers
57 views

Derivation: Discerning difference between arithmetic expression with parenthesis versus without using abstract syntax trees

I am trying to illustrate the expression: ( 3 * 4 + 5 * 6 + 7 ) using an abstract syntax tree. I have already illustrated the expression: ( 3 * (4 + 5) * (6 + 7) ). Could someone please illustrate ...
2
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1answer
39 views

Equivalence of regular expression

Let $ A = \{a,b\}$ be an alphabet. Please hint me with show, that this regexes are equivalent. That means, we should show that: $L(e_1 )= L(e_2)$ 1) $(a^*b)^*a^* = (a+b^*)^*$ 2) $(a+b^*)^* = ...
1
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1answer
35 views

Difference between regular and not regular languages

I don't understand the difference, in classes I've seen the pumping lemma for regular languages and I know how to apply it to demonstrate whether a language is regular or not, but I feel that I don't ...
2
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1answer
99 views

NFA to DFA and Regular Expression

The truth is that my teacher gave us a homework, and I wanted to ask you if I did this right. What I have to do is answer the following questions given the following NFA. Why is this an NFA? What ...
1
vote
1answer
167 views

Find regular expression for a given language

I need to find a regular expression for the following language: $$ \Sigma = {\{a,b,c}\} $$ define $L$ to be the language of all words over $\Sigma$ that contain the substring $aba$ odd number of ...
0
votes
1answer
101 views

Proving an operation is closed under regular languages

Following operation is defined over languages where $n \in \mathbb{N} :$ $L \ominus n = \lbrace s \in \sum^* | \exists s^{'} \in \sum^* (length(s^{'})=n,ss^{'} \in L) \rbrace$ Meaning that $L ...
1
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2answers
59 views

Proving {0^n 1^n 2^n | n >= 0} is not regular

This is not a homework assignment, but something I'm reviewing. I need to prove that $0^n 1^n 2^n$ where $n \geq 0$ is not regular (Just the DFA, not related to CFG). I feel like this is similar to ...
0
votes
1answer
103 views

Convert the regular expression to a NFA

I have to convert the following regular expressions to a NFA: $$(0 \cup 1)^{\star} 000 (0 \cup 1)^{\star}$$ $$(((00)^{\star} (11)) \cup 01)^{\star}$$ $$\emptyset^{\star}$$ $$a(abb)^{\star} \cup ...
1
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1answer
59 views

Write the regular expression of the language that the DFA accepts.

I am given a DFA and I have tried to write the regular expression of the language that it accepts. This is the DFA that I am given: I have found some words that the DFA accepts: ...
0
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1answer
175 views

Proving that two expressions are equivalent

So, I'm working through some proof exercises, and one of the questions is about the following regular expression: (a|b)* = a*(a|b)* if they are equivalent, prove ...
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2answers
38 views

Finding the regular expression

I have the problem below: I need to find the regular expression of the set of strings where $n(a)+n(b)$ is an even number (where $n(a)$ is the number of $a$'s and $n(b)$ is the number of $b$'s) .. I ...
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0answers
31 views

One-to-one correspondance between regular sets

I have problem with one-to-one correspondance "One-to-one correspondence with the set (B) of all tags possible being represented with their binary representation (i.e. 0, 01, 00, 010101, 11000, ...
1
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1answer
47 views

Regular expressions

I have this assignment and I have to prove that $$ (b+aa^* b)+(b+aa^* b)(a+ba^* b)^* (a+ba^* b) = a^* b(a+ba^* a)b^* $$ How do I prove this? What I have is this: $$\begin{align} \text{LHS} ...
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0answers
36 views

Regular expressions and equality

Is the equality true or false? $(r^*s^*)=(r+s)^*$ My Approach: Assume the alphabet used is {0,1}$^*$ Equality is false: If r = 0 and s = 1 Then if 0101 $∈$ $(0 + 1)^*$ this is true because ...
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1answer
67 views

Proving Reversal of a Language in Recursive Way

We define the $reverse$ of a string as follows: $(x_1x_2...x_n)^R=x_nx_{n-1}...x_1$ where $x_1,x_2,...,x_n \in \Sigma$. We can also define the reverse of a language by $L^R= \lbrace s' | \exists s ...
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1answer
21 views

Clarification on Lemma problem

I have trouble understanding this question. I have no idea where to start. Let $A$ be the set of palindromes over $\{a, b\}$. Suppose you are trying to prove that $A$ is not regular using the ...
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0answers
54 views

Does there exist a regular expression for a series of points?

If I was looking for a certain "shape" or "pattern" in a simple line chart is there a way to describe the series of points that would make up this "shape"? Example: If I had a line chart and I was ...
0
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5answers
69 views

Regular Expression for Simple Language

I'm having trouble writing a regular expression given the following $\{a, b, c\}$ which produces the set of strings of length 3. I don't really understand how to restrict the length of the string. ...