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1answer
42 views

Question About Pumping Lemma used on a FA

I am learning about pumping lemma and I am trying to solve a problem. I need to use pumping lemma to show that: the Language L(M) defined by the following machine is infinite. Here is the dfa: ...
0
votes
2answers
117 views

Regex for strings with at least three unique characters

I'm trying to represent some string conditions in terms of regex. One of those conditions I find hard to transform is that the string must have at least three different characters. So is there any ...
0
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3answers
2k views

Regex for strings with no three identical consecutive characters

I wanna ask what the regular expression for the strings having the property in the title should be. For binary string with no three consecutive 0, it's quite a simple regex ...
2
votes
1answer
731 views

Complement of a regular expression?

What is the regex for the complement of $r = b^*(ab + a^* + abb(b^+))^*$ ? I am thinking $(a+b)^*(abb)^+a^* $ since anything that contains $abb$ and is not followed by $b$'s would not be accepted ...
2
votes
1answer
1k views

Proof of Equivalence of NFA and DFA, quick question about the setup

I am looking at the proof of equivalence of non determinstic finite automata(NFA) and deterministc finite automata(DFA). I am have a small quesion about the construction: Let ...
4
votes
0answers
91 views

How to write a regular expression?

I am trying to write a regular expression for the set of all strings in Σ* that starts with an even number of b's and contains at most two a's. The language contains only a's and b'. This is what I ...
0
votes
2answers
141 views

Show that, given regular expression $R$, we can decide whether $L(R)$ is prefix-free

Suppose language $L$ is called prefix-free if no member is a proper prefix of another. For instance, cat is a proper prefix of category and so $L = \{cat,category,ego,go,rye\}$ is not prefix free. ...
0
votes
1answer
120 views

how did they get this answer for the words that don't have bba and abb?

I am looking at the answer in solution manual which asked , ...
0
votes
1answer
50 views

Struggling with Proof Writing. Simple question for demostration.

I am practicing writing proofs over regular expressions. Here is the question: Show that $(r\cup \varepsilon)^*= r^*$, where $r$ is a string. Intuitively, the left hand side is the concatenation of ...
1
vote
1answer
41 views

Give a regular expression for $A = \{1^{k}y|k \geq 1, y \in \{0,1\}^{*}$ and $y$ contains at least $k$ $1$'s $\}$

The regular expression that is given is $1(0 \cup 1)^{*}10^{*}$. I'm having trouble realizing why this regular expression describes the language given. For example, the string (for $k$ = 4) $1111$ ...
0
votes
1answer
25 views

Regular Expression Reading

I'm trying to figure out what this regular expression reads as. The regular expression is the following: (0(1 + 2) * 00*) (+ = union) (* = zero or many). I believe this reads as: 0 concatenated ...
1
vote
1answer
48 views

Pumping Lemma Squares Proof Explanation

I'm looking for some help understand this perfect squares proof using the pumping lemma. Here is the proof: I don't understand how n^2 + k < n^2 + n towards the end of the proof. Would anyone ...
0
votes
1answer
50 views

Expressions for $(AB)^R$, $(A \cap B)^R$, $(A \cup B)^R$

For any language A, let $A^R$ be $\{x^R \mid x \in A\}$. Then, for arbitrary languages $A$ and $B$, explicitly write down the expressions for $(AB)^R$, $(A \cap B)^R$, $(A \cup B)^R$. I am not really ...
0
votes
2answers
398 views

Regular expression and DFA/NFA questions

If a language L is generated by a regular expression, then L is recognized by a DFA. I think this is true, because regular expressions describe regular languages, those of which are exactly ...
1
vote
1answer
37 views

Is the language L regular?

Could you tell me if the language $L=\{a^ib^j:i+j=k, k \geq 2 \}$ is regular? Do I have to find a regular expression for this language? Or what can I do to check if $L$ is regular or not?
-1
votes
1answer
52 views

Finding the wrong regular expression

Which one of the following regular expressions does not define the language of all strings that ends with a. $(a + b)^*a$ $b^*aa^*(bb^*aa^*)^*$ $[a(ba)^* + b(ab)^*](a + b)^*a$ $(b + aa^*b)^*a(a + ...
0
votes
1answer
66 views

find a regular expression for a given language

It is given that $\Sigma=\{1,2,4,5,7,9\}$ and $L=\{w: w \in \Sigma^{*} \text{ ,w gets divided completely by }5\}$. Could you help me to find a regular expression for this language?
0
votes
1answer
1k views

regular expression that dont have both substrings bba and abb

All the words that dont have both the substrings bba and abb ‘words that do not have both substrings…’ means that words may have one or the other - just not both (i.e. not abba or bbaabb). I tried ...
3
votes
5answers
85 views

Expression for a bounded function

I have a bounded function, $$ y= \begin{cases} 1 & \text{if $x>1$} \\ x & \text{if $0\leq x\leq 1$}\\ 0 &\text{if $x < 0$} \end{cases} $$ Does anyone ...
2
votes
2answers
100 views

Regular Expression Notation

I'm doing a theory of computation course and can't for the life of me find any good resource that will tell me how a regular expression such as (a+b)* converts to set form. I've thought of a binary ...
0
votes
1answer
85 views

Finding regular expressions

I'm given the DFA shown below and need to find regular expressions for the following languages: $L_{1,2}^0, L_{2,1}^6, L_{2,5}^4, L_{2,3}^5, L_{1,3}^5$. The language $L_{p,q}^r$ is defined as ...
0
votes
1answer
39 views

Is this a regular language? Number of a's greater than $k$

Prove/disprove: $L = \{ w \mid |w|_a \geq 2k \}$, where $\Sigma = \{ a,b\}$ and $k$ is a constant, is a regular language. Intuitively I am saying yes, it is a regular language. But I don't ...
1
vote
1answer
247 views

Check if a regex is ambiguous

I wonder if there is a way to check the ambiguity of a regular expression automatically. A regex is considered ambiguous if there is an string which can be matched by more that one ways from the ...
0
votes
0answers
28 views

productions with identical right hand sides for different nonterminals

Can a regular grammar contain two productions with identical right hand sides? I know in context free grammars shift reduce parsers issue reduce reduce conflicts when smth like this happens. What are ...
2
votes
1answer
81 views

Build regular expression from language

I have the following language: L = {w $\in$ {a,b}* | aa is not part of w}. I have to construct a regular grammar from this language and I thought about first finding the regular expression from the ...
2
votes
2answers
2k views

How can concatenating empty sets (languages) result in a set containing empty string?

In the book "Introduction to the Theory of Computation" by Michael Sipser, in the section 1.3 Regular Expressions: The symbol ε represents the emty string, which may be a valid element of a language: ...
0
votes
2answers
66 views

Determine whether $L=\{w:|w|_a=2^n+273\text{ for }n\in \mathbb{N}\}$ is regular.

Given the alphabet $\Sigma=\{a, b\}$ and for the next Language $L=\{w:|w|_a=2^n+273\text{ for }n\in \mathbb{N}\}$ determine whether the language is regular. Firstly, I think this language is regular. ...
0
votes
1answer
43 views

Prove equivalence of two regular expressions.

I am wondering if there is a standard way to prove that two regular expressions are equivalent. I have tried to prove, given two regular expressions $r$ and $s$, that $L(r) \subseteq L(s)$ and $L(s) ...
0
votes
0answers
36 views

How to write a Regular Expression

I have seen that the regular expression for the set of strings beginning with a and ending with b is written as a(a+b)*b Can some one tell me how to write this
0
votes
1answer
74 views

Which strings belong to the regular set represented by the regular expression (1∗01∗0)?

I know the string should be like 1…101…10, but not sure how to describe it. Can anyone help me?
1
vote
1answer
113 views

Complement of a Set of Strings in a Language

Suppose $B= \{ 0^n1^m2^{n-m}:\, n\ge m\ge 0 \}$ Is the complement $\overline B = \{ 0^n1^m:\, 0\le n\lt m\}$? Or is it the universe of all possible strings (including all strings with symbols ...
0
votes
1answer
88 views

Proving Equivalence of DFA and NFA

Im trying to learn Equivalence of DFA and NFA.The problem is that in the below explanation Q' is given as the power set of Q.But this statement seems to be contradictory to the previous statement ...
0
votes
1answer
88 views

Find Regular Grammar from NFA

I'm currently doing some self study to improve my half-forgotten college theory of comp skills. I'm going over some problems from an old book and it asks you to find a regular grammar for the ...
1
vote
1answer
1k views

Build regular grammar from regular expression

Is there an algorithm for creating a regular grammar directly from a regular expression? All the discussions and notes I found so far go through an intermediary step of creating an FA for the reg ex ...
2
votes
0answers
280 views

Regular Expression For Set of Strings Not Containing OOO

The following is my attempt at coming up with a regular expression for the set of binary strings that do not contain $000$: $(1 + 01 + 001)^*(\epsilon + 0 + 00)$ I'm going to need it for a ...
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2answers
100 views

Deterministic Finite Automata with finite strings

How could I prove that every language with a finite number of strings is the language of some DFA?
0
votes
1answer
601 views

Set of Binary Strings Corresponding To a Regular Expression

$(1 + 01)^*(0 + 01)^*$ I'm thinking {set of all binary strings} $-$ {set of binary strings that begin with 00 and contain 11} Would this be correct?
1
vote
1answer
42 views

Regular Expression that accepts a language L

Given, $L=\{ x \in\{0,\,1\}^* | x=0^n1^m \text{ and }n+m\text{ is a multiple of }3\}$ give a regexp that accepts the language. My thoughts are: $(000)^*(\epsilon + 001 + 011)(111)^*$ Is this right? ...
0
votes
1answer
308 views

Induction to prove regular expression

Prove that is if S and T are any regular expressions over the one-letter alphabet, (for example: Σ = {a}), and if n is any natural, then the languages (ST)^n and (S^n)(T^n) are equal. I have to use ...
0
votes
1answer
783 views

Palindrome Decidable by DFA

Here's a problem a professor I was talking with gave to me to see how people solve. How would you solve this? A string in {a,...,z}* is said to be a palindrome if it is equal to its own reversal. Is ...
1
vote
1answer
82 views

About described DFA

I need to find DFA (or NFA, $\epsilon$-NFA, it's not improtant (I know how to convert between them)) that accept all strings of $0$'s and $1$'s such that every block of five consecutive symbols ...
1
vote
1answer
52 views

Myhill-Nerode Theorem with constraint

I am trying to to understand the Myhill-Nerode Theorem with the example. $L = \{{0^i1^j}|\ j > i\}$ I have read some article but still cannot fully understand,what I know about is that I have to ...
0
votes
1answer
76 views

Prove/Disprove: $vwvw=vvww$ iff $\{v\}^*\{w\}^*=\{vw\}^*$

Let $\Sigma$ be an alphabet and $v,w\in \Sigma^*$. I'm trying to prove that: $$vwvw=vvww\quad\text{iff}\quad\{v\}^*\{w\}^*=\{vw\}^*.$$ I tried to do it by induction, with no success. Any help will ...
1
vote
1answer
44 views

Mathematical expression of largest $k$ numbers from $n$ numbers $(n>k)$

Can someone provide me a Mathematical expression of largest $k$ numbers from $n$ numbers $(n>k)$ eg $S$ is a 3x3 matrix with [6 8 5 ; 3 4 6 ; 9 0 5] where $n$ = 9 (elements) and I need to ...
1
vote
1answer
129 views

Translate a regular grammar to a regular expression

I want to translate the following grammar into a regular expression: Set of variables V := {S,T} Set of terminals Σ := {a,b} Set of relations S → "" S → aS S → bT T → ...
1
vote
1answer
342 views

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. ...
2
votes
1answer
64 views

Regular expression for language

Let's have a language $L=\{\omega\in\{a,b,c\}^* | \omega $ contains $ab$ and does not contain $ba\}$ make a regular expression for this language. I've ended up with this one ...
0
votes
2answers
48 views

Concatenation of strings

We have two strings A and B. We have to find if for some n,m A concatenated n times equals B concatenated m times or not. I have made an interesting observation but am unable to prove it.It appears ...
1
vote
1answer
110 views

Question about Regular Expressions, DFA and relations

I have a few questions about discrete math, I can't fully grasp these concepts. For regular expression, what does the U symbol mean, at first I thought it meant that it was similar to or, for example ...
0
votes
2answers
100 views

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 ...