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1answer
37 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: ...
3
votes
0answers
64 views

This proof in my textbook involving the pumping lemma appears incorrect - is it?

It states Let $B$ be the language $\{0^n1^n2^n | n \geq 0\}$. We use the pumping lemma to prove that $B$ is not regular. The proof is by contradiction. Assume to the contrary that $B$ is regular. ...
0
votes
2answers
74 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 ...
3
votes
3answers
81 views

Is $L = \{(x,y,z) | x+y=z\}$ a regular language?

Suppose $x,y,z$ are coded as decimal or their binary representations in an appropriate DFA. Is $L$ regular? My intuition tells me that the answer is no, because there are infinitely many combinations ...
0
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2answers
1k 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 ...
1
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1answer
378 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 ...
3
votes
1answer
35 views

How do you prove that the set of neighbors of $L$ is regular if $L$ is regular?

I know that a regular language can be made into a DFA, so can I just make a DFA for the regular language? Also, someone told me I should make a e-NFA from the DFA, but I don't see what would be the ...
2
votes
1answer
685 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 ...
2
votes
1answer
80 views

Pumping Lemma for regular languages proof template

http://www.cs.uiuc.edu/class/fa06/cs273/Lectures/pumping-lemma/pumping-lemma.html So, I went to that site and it says: $w = xyz$ $|xy| \leq p$ $|y| \geq 1$ for all $i$, $xy^iz$ is in ...
0
votes
1answer
225 views

Show that two disjoint languages are not separable

What is the general method to show that two disjoint languages are not separable? As an example, suppose we have: $A = \{\langle M \rangle : M ( \langle M \rangle )$ halts and says ACCEPT$\}$ $B = ...
0
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1answer
57 views

showing language that is non-regular using pumping lemma

I am looking over pumping lemma and the author is using it to show that the language is non-regular. {a^n b^n a^n} = {aba aabbaa aaabbbaaa........} Is there ...
0
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1answer
48 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
2answers
145 views

Prove the language $\{a^k b^l : k \neq l \}$ is not regular

Prove that the following language is not regular: $$L=\{a^k b^l : k,l \ge0, k\ne l\}$$ The problem is that I should use "distinguished states" not the pumping lemma, which is usually used for such ...
1
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1answer
46 views

Regular languages and intersection

Let L be a language and R an infinite regular one. If L intersection R is a regular language, then L is a regular one too?
1
vote
1answer
56 views

Question about equlaity of two language, simple but tricky.

I found the following question tricky: If $A$ is a language, when will $A^*=A^+$? By definition, $$A^* = \bigcup^{\infty}_{i=0}A^i = A^0 \cup A^1 \cup A^2 \cup \cdots$$ $$A^+ = ...
1
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2answers
24 views

A question about operations on languages.

I come across this problem on a book. It states that: for languages A and B, $(A\cup B)^* = (A^*B^*)^*$. I know that the definition of star closure is $\left(\bigcup^{\infty}_{i=1}\right)A^i$. But so ...
2
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1answer
48 views

A correct proof for this pumping lemma example?

Given the language $L = \{0^{2^n} | n \geq 1\}$ So, the language contains all strings that have $2^n$ $0$s. First of all I take $z = a^{2^p}$ where $p$ is the constant guaranteed by the pumping ...
0
votes
1answer
41 views

Regular language restricted to smaller alphabet is regular

Let $L$ be a regular language on some alphabet $\Sigma$, and let $\Sigma_1 \subset \Sigma$ be a smaller alphabet. Consider $L_1$ the subset of $L$ whose elements are made up only of symbols from ...
0
votes
1answer
24 views

Is the language regular or contextfree?

Could you tell me if the language $$L=\{ w \in \{a,b,c\}^*: $$$$\text{there is at least one time the substring abc and none of the symbols a,b,c is repeated three times} \}$$ is regular or ...
0
votes
1answer
30 views

Use closure properties for the language $L=\{a^kb^l:|k-l| \leq 100 \}$

Given the language $$L=\{a^kb^l:|k-l| \leq 100 \}$$ I have to show that $L$ is regular or context free using closure properties. I have done the following: The language is regular. Let $k>l$, then ...
0
votes
1answer
28 views

How can I show that the language is regular using the closure properties?

How can I show that the language $L=\{ w \in \{a,b\}^*: \text{ the word w contains an even number of a and an odd number of b} \}$ is regular using the closure properties?
1
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1answer
44 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
2answers
345 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
36 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?
2
votes
1answer
102 views

Are languages regular if their concatenation is regular?

Let $A, B \subset \Sigma^*$ be languages. If the concatenation product $AB$ is regular, are $A$ and $B$ necessarily regular? I'm inclined to think this is true since the regular language $AB$ has a ...
0
votes
1answer
40 views

Is it necessary that X is also regular?

Given that $L$ is a regular language and $X \subseteq L$,does $X$ have to be also regular?
1
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1answer
25 views

DFA for {any sequence of a and b, between two consecutive “b” there are maximum 3 “a”}

I have tried to draw a deterministic finite automaton for the language L={any sequence of a and b, between two consecutive "b" there are maximum 3 "a"}: Is it correct?
1
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3answers
125 views

NFA for $(ab|a)^{*}$ using only 2 states

In Introduction to the Theory of Computation by Michael Sipser, there's an example which shows how to convert the regular expression $ (ab|a)^{*}$ into an NFA. The "standard" method results in 8 ...
1
vote
1answer
59 views

is this language regular or not?

I have problem with this language $$L = \{ a^n b^m : \text{$n+m$ is odd} \}$$ is it regular or not My Solution I used pumping lemma, w = a^2p b^2p+1 (the same for a^2p+1 b^2m ) ...
0
votes
1answer
80 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 ...
1
vote
1answer
170 views

Finding Nerode equivalence classes

How am I supposed to find the equivalence classes of a Language? What should I think? For instance, having a language $$L =\{a^n b^m \mid n,m \ge 0, (m+n) \bmod2=0)\}$$ I can have: $[a^n]$ with ...
1
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3answers
56 views

regular language question

Good afternoon everyone; I am stuck with a question I could not find and answer by myself I hope you can help me. My question is The language L = {w : w {a,b}*, |w| is odd, w has exactly one b}. ...
0
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1answer
35 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 ...
0
votes
1answer
52 views

Show that the language is regular modifying the DFA

Let L be a regular language. How can I show that the language $\text{Suffix}(L)=\{w \in \Sigma^* \mid \text{ there is a $x \in \Sigma^*$ so that }xw \in L\}$ is also regular? How can I modify the DFA ...
1
vote
1answer
156 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 ...
1
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0answers
34 views

Why every regular language is in $\text{TIME}(n)$?

How can I prove that every regular language $R$ has linear time complexity, i.e. every regular language satisfies $$R \in \text{TIME}(n)$$
1
vote
1answer
217 views

DFA for Boolean Formula

Let $ f\left( b_{1}, \dots , b_{n} \right)$ be a boolean function. Define $S_{f} = \{\left( b_{1}, \dots , b_{n} \right): f\left( b_{1}, \dots , b_{n} \right)=1; b_{i} \in \{0,1\}, 1\leq i \leq n \}$ ...
1
vote
1answer
21 views

Language regularity implications

I have to decide whether this implications are true or false and prove it. Will you help me? $L.\{a,b\}^{*}$ is regular $\implies$ $L$ is regular $L.\{a,b\}^{*}$ is not regular $\implies$ $L$ is not ...
3
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0answers
83 views

Applying the Myhill-Nerode Theorem

Consider the language $$L=\{x y^{(n)} z y^{(n)} w: x,z,w \in \Sigma^*, y \in \Sigma, z\text{ does not contain }y, n \geq 0 \}.$$ To show that the language is not regular using the Myhill-Nerode ...
0
votes
1answer
75 views

Show that the language is regular without a DFA

How can I show that the language {$w \epsilon$ {$0,1$}$^{*}:$ the word $w$ contains neither the (sub)string $000$ nor $11$} is regular without using a DFA? (Using the closure properties)
0
votes
1answer
64 views

Formal Languages - Prefix on Language

Given a language $L$ over an alphabet $\Sigma$, we say that $u,v \in \Sigma^*$ are prefix equivalent over $L$, denoted $u \sim_L v$, if $uw \in L \iff vw \in L$ holds for all $w \in \Sigma^*$. Is ...
0
votes
1answer
107 views

Pumping lemma-regular language

Show that the language $L = \{w \mid w \in \{a,b\}^{*}\}$ is not regular by using the following version of Pumping Lemma: Let $L$ be the language, which has an infinite number of words, then there ...
0
votes
1answer
38 views

Show that the language is regular

Given a regular language L on the input alphabet Σ, and X a subset of Σ*, show that the language {$w$:$w$ $\epsilon$ L, there is a x $\epsilon$ X so that $wx$ $\epsilon$ L} is also regular. Could you ...
3
votes
1answer
37 views

Irregular $a^nb^n$

We studied in class that regular languages closed under intersection. My question is : if we take the irregular language $L =$ {$a^nb^n : n\geq 0$} and the regular finite language $L' = \{a^3 ...
0
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0answers
27 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
56 views

Language concatenation

We learned in class that the regular languages are closed under concatenation (e.g $L_1L_2 =\{ w_1w_2 : w_1 \in L_1,w_2 \in L_2\}$ is a regular language if $L_1$ and $L_2$ are also regular ...
0
votes
1answer
20 views

proving regular language

let $L$ be a language over the alphabet $\{a,b\}$ that maintains that for each $w \in L$ ,the difference in absolute between the number of apearences of the letter $a$ and the number of apearences ...
1
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1answer
42 views

Pumping lemma $c^2a^nb^n$

I'm trying to prove that the following language is not regular via the Pumping Lemma. But I don't know, why is my procedure wrong (choosen word is incorrect according to my teacher). $$L= c^+ \cdot ...
4
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1answer
672 views

Routing Automaton

Is there a formal proof for the following question? For a DFA $M= (Q,\Sigma,\delta,s,A)$, we extend the function $\delta : Q \times \Sigma^* \to Q$, such that every $w \in \Sigma^* $, ...