Questions about properties of the class of regular languages and individual languages.

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1answer
30 views

How to improve the accuracy of automatic conflict resolution?

A little background information from my previous question:http://english.stackexchange.com/questions/318528/conflict-resolution-how-to-decide-if-two-words-are-generally-unmistakable When a court ...
1
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1answer
43 views

Show that language generated by grammar is regular

We have grammar with nonterminals $ X_1,...X_n$ terminals $V_t$ and rewriting rules of form: $X_i \rightarrow a \in V_t $ $X_i \rightarrow X_jX_k, \ i \ge j , \ i > k $ How can I show that ...
7
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2answers
1k views

Will $L = \{a^* b^*\}$ be classified as a regular language?

Will $L = \{a^* b^*\}$ be classified as a regular language? I am confused because I know that $L = \{a^n b^n\}$ is not regular. What difference does the kleene star make?
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2answers
53 views

Can a regular language have uncountably many strings?

Obviously it can have a countably infinite number of strings. (Take the language descibed by the regular expression 0* as an example.) But can a RL have uncountably many strings? I'm leaning toward ...
0
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2answers
29 views

Is the given language finite or infinite?

I have an idea regarding whether this language is finite or not, but for some reason I am still having some issues regarding exactly grasping what makes a language finite or infinite. I know that ...
0
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2answers
63 views

If L is a regular language, how to prove that L' is also regular?

I've been trying to construct a proof of the following statement the whole day but I got stuck: If $L$ is a regular language, the language $L_{}{'}$ consisting of all words in $L$ containing the ...
0
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0answers
24 views

Is the language of all DFAs that accept the empty language regular?

Is $E_{DFA}$ in the class of regular languages? $\qquad E_{DFA} = \{ \langle D \rangle \mid D \text{ is a DFA }, L(D) = \emptyset\}$ My argument is that it is because all of the DFAs in $E_{DFA}$ ...
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1answer
31 views

How similar are two DFAs? -not just binary equivalence- [on hold]

Are there any measures to compute similarity (or distance) between two DFAs? If yes, which are the mainly references? NB: I need a measure of similarity, and not binary equivalence test.
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1answer
42 views

Languages having only one Myhill–Nerode equivalence class

Consider the alphabet $\{a,b\}$, for which languages does the Myhill–Nerode equivalence relation have exactly one class? From what I understand about equivalence classes, each state is ...
-1
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1answer
22 views

Give regular expression on language [duplicate]

What is a regular expression for $L_1=\{a^{2n} b^{3m+1} \mid n \geq 1, m \geq 0\}$?
0
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1answer
25 views

Is the union of a non-regular and a regular language regular?

I am studying Automata and stuck in a question that says: Is the following a regular set {a^p, where p is prime} U {even-length strings}? As we see here this language consists of two sub-languages. ...
0
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2answers
57 views

Prove that the language of squares is not regular using homomorphism

If a language like $L$ is regular, then any homomorphism of $L$ is regular too. So, if $h(L)$ is not regular, then we can conclude that $L$ is not regular. Assume that the language $L=\{yy:y \in ...
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1answer
37 views

What's the difference between the concatenation and union of symbols within a language

I feel like I'm confusing myself perhaps but I'm having a bit of trouble figuring out how exactly this language works. I'm given the following regular expression (a + b)* (abba* + (ab)*ba) Can ...
1
vote
1answer
70 views

Show language is not regular

Show that the following languages are not regular in two ways: first by using closure properties then by using the Pumping lemma: $$\text{(1) L1} = {a^n b^k c^{n+k} : n >= 0; k >= 0}$$ ...
2
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1answer
65 views

Show L1 /L2 is regular [duplicate]

Let $L_1$ and $L_2$ be two languages over an alphabet $\Sigma$. The quotient of $L_1$ and $L_2$ is the language $L_1/L_2 = \{x : \exists y \in L_2, xy \in L_1\}$ Show that if $L_1$ is ...
2
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1answer
85 views

Proving that the scramble of a regular language is context-free

For strings $w$ and $t$, if they have the same length and comprise the same characters (namely, they are two permutations of these characters), then $w\sim t$. For a string $w$, define an operator ...
2
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1answer
34 views

Difference between a minimal DFA and a canonical DFA

given a language L,a DFA M that recognize L is minimal if M is the DFA with the minimum number of states. In order for this to happen M does not have neither unreachable nor equivalent states. The ...
0
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1answer
48 views

If L is a regular language then the language replace(L,σ,τ) is also regular

I am stuck at the following problem: Prove that if $L$ is a regular language over some alphabet $\Sigma$ and that $\sigma, \tau \in \Sigma$, Then the language $replace(L,\sigma,\tau)$ is regular. ...
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0answers
25 views

If a CFG has a word with length more than its variables then the language of it is infinite?

Grammar G have n variables in normal Chomsky form, It can build a word with length w, using m rules. Which disprove each of following statements: If w > n then the language of the grammar G is ...
2
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1answer
25 views

Can a non-regular language be made regular via concatenation when they don't share characters?

So this is a follow-on question to my other question (Can we make a non-regular language regular via concatentation?). Given the following, $L = \{0^n1^m2^m \mid n>1, m>1\}$ $A = \{0^n \mid ...
4
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1answer
40 views

How do I show that an equivalence class of a language containing an empty string is infinite

The question is as follows: Let $L$ be a language (not necessarily regular) over an alphabet. Show that if the equivalence class containing the empty string $[ \epsilon ]$ is not $\{ \epsilon ...
7
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5answers
889 views

Can we make a non-regular language regular via concatentation?

My question is basically given three languages A, B and L, where L is A and B concatenated together and B is proven to be non regular, is it possible to find an A that makes L regular?
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1answer
136 views

What is the difference between formal language, regular language and regular expression? [closed]

I want to know the difference between these three languages and it would be great if you would give some examples as well, thank you. :)
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2answers
34 views

Closure under reversal of regular languages: Proof using Automata

I have been studying the closure properties of regular languages, referencing the book Introduction to Automata Theory, Languages, and Computation by John E. Hopcroft and Jeffery D. Ullman. Under the ...
1
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1answer
27 views

A regular expression for an automaton which accepts strings with no more than 3 consecutive zeros [duplicate]

This is the automaton I want to find the regular expression for: As you see, states Q1 to Q4 are accepted and Q5 is a kind of trap. This automaton accepts strings that have no more than 3 ...
1
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1answer
48 views

Showing the the language represented by a set is regular

Is the language $L = \{ w \mid w $ is $ 3^n - 1 $ in some given representation $, n > 0 \}$ regular? I know that it is regular. If each element in $L$ is represented as decimal numbers, $L = \{ 2, ...
2
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1answer
48 views

How to pick w for the Pumping lemma if the language has no clear pattern?

I'm trying to understanding using the pumping lemma to prove that a language is not regular. I sort of understand how it works when the language describes strings with a particular form, like in this ...
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1answer
56 views

Regular expression of a given language [closed]

Could somebody please confirm if a regular expression of language: $$ L := \{b(ab)^n a^m \mid n, m \geq 0\} $$ is $$\{b, (ab)^* a^*\}? $$ And if not, could somebody please tell me why?
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1answer
69 views

Converting a language to a PDA?

I am trying to convert the follow language $$L = \{0^m1^n \ | \ 0 \le m \le n \le 2m\}$$ We have an exam in 2 days and the professor didn't teach us much about PDA's. They will be on the test though ...
2
votes
2answers
52 views

Proving a CFG is ambiguous?

I have a CFG: S --> 0S1S | 1S0S | ε I'm trying to prove that it is ambiguous, but the steps to proving so are confusing me. So if I pick a string, let's say ...
3
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1answer
88 views

Non-regularity of the set of primes in unary encoding using Myhill-Nerode

I have found many proofs for this using pumping lemma, I'm curious of how to proof it via Myhill-Nerode theorem. Suppose $L= \{a^p \mid p \text{ is prime}\}$ is regular. Then we have congruence such ...
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0answers
22 views

How do I prove a language is regular? [duplicate]

I've done a lot of research on this topic, but still don't feel very confident about it. Let's say the example is: For a language L over an Σ, define N(L)={w∈Σ∗: wk∈L for some k∈Σ∗}. Prove that, if L ...
1
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1answer
84 views

Regular and Non-Regular Language

My friends and I are taking a formal languages class and for one of our homework questions we have to prove if these languages are regular: 1) L = {apaqi : p and q are fixed integer values, i >= 0} ...
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1answer
78 views

Confusion in Pumping Lemma

I would like to know whether we could pump $ba$ into $bbba$ where x=$b$,y=a,z=$\epsilon$ using the finite state machine given in the image 1. For example as given in this image 2 where the string ...
2
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2answers
68 views

Regular language? Union of the dictionary and an non-regular language

I'm attempting to figure out if a union of two languages is regular. $$ L_1 = \{all\ the\ words\ in\ the\ Oxford\ dictionary\} \\ L_2 = \{w : w\ has\ twice\ as\ many\ a's\ as\ b's\} $$ $L_2$ is well ...
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2answers
50 views

DFA for $L_1={w:(n_a(w)+2n_b(w)) mod 3<2}$ and $L_2=\{w:(n_a(w)+2n_b(w))\text{mod 3}<2\}$

I stumbled upon this file on scribd, which gave some interesting problems on constructing DFA. So I went on solving them, until I came across one for which result DFA is not drawn but are described in ...
3
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1answer
63 views

If L is regular, so is L2 (proof using closure properties)

I've got a question that asks me to explain how if a language L is regular, then so is: $M=\{s \in \{a, b\}^* |\ \exists\ t \in L\ such\ that\ |s|_a = |t|_a\}$ I believe I would have to get M into ...
5
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1answer
52 views

What can be said in general about a homomorphism between two regular languages?

In other words: is a homomorphism always guaranteed to exist between two arbitrary regular languages? If not (which I suspect), are there only a finite number of classes of languages, for which we can ...
7
votes
5answers
620 views

Is there a known method for constructing a grammar given a finite set of finite strings?

From my reading it seems that most grammars are concerned with generating an infinite number of strings. What if you worked the other way around? If given n strings of m length, it should be possible ...
1
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1answer
48 views

Regular languages and constructing a regular grammar

I'm pretty new to computer science and just read about the concept of grammars. Now, I have a practical problem to solve. Here is the alphabet {a, b, c, d}. How ...
3
votes
1answer
77 views

Index of a language and its reversal [duplicate]

The index of a language is the number of Myhill-Nerode classes that it has. It is also equal to the number of states in the minimal DFA for the language. What is an example of a language that has a ...
10
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3answers
2k views

Is there any uncountable Turing decidable language?

There are many(and I mean many) countable languages which are Turing-decidable. Can any uncountable language be Turing decidable?
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3answers
81 views

Regular Expression simplification

Does $(0 + 10^{*}1)^{*}$ simplify to the following language: Set of all binary strings with even number of ones. In specific, does the * inside the brackets get evaluated first or the outer * gets ...
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1answer
49 views

Proving that a programming language is not regular

I am wanting to show that the C programming language is not a regular language. The alphabet would be ASCII characters and comments, strings, char can contain arbitrary characters. Would I best ...
4
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1answer
74 views

Proving that English is not a regular language

I am wanting to try and prove that the English language is not regular. The alphabet is the set of all words in the English dictionary. Looking at sentences, I was able to use this pattern of ...
0
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0answers
15 views

Proving right quotient of two languages [duplicate]

I know that if a language $L_1$ and a language $L_2$ are regular, then $L1/L2$ is regular. When we construct a DFA $M'=(Q, \Sigma, \delta, q_0, F)$, for each state $i$ we can make $i$ the start ...
0
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1answer
31 views

Checking my understanding of right quotient

So I am trying to fully understand the concept of quotient languages. I will give some examples, let me know if this is correct: Say that ...
0
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1answer
195 views

Proving $A$ avoiding $B$ regular if $A$ and $B$ are regular

Suppose we define an operation such that $$A \text{ avoiding } B = \{w \in A \mid w\text{ has no substring in }B\}\,.$$ How can I prove that, if $A$ and $B$ are regular then $A\text{ avoiding }B$ ...
0
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2answers
203 views

How do you find an infinite regular language that is a subset of a non-regular language?

In order to do this, we would probably need the non-regular language to be infinite as well, then find some definition for the non-regular language in order to fulfill the requirement, but I don't ...
0
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1answer
49 views

Proving following regular expressions equal to one another?

How would I go about proving the following two regular expressions are equal to one another: ( a + b )* a ( a + b )* b( a + b )* = (a + b)* ab(a + b)* I can ...