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Questions tagged [regular-languages]

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

3
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3answers
107 views

If $L$ is a regular language, then $s(L)$ is also regular

...where $s$ is a substitution that replaces each symbol of each string in $L$ with a regular expression. For example, if $L=a^*b$ and $s(a) =ab, s(b) = b^*$, we have $s(L) = (ab)^*b^*$. My ...
0
votes
2answers
124 views

How does modulus affect the regularity of language?

the question is as follows, further the notation used are standard as used in theory of computation $$L = \big\{ w : w \in \{a,b\}^*,\ |n(a) - n(b)| = 2k\}\,.$$ Beware 'K' is not a fixed integer its ...
0
votes
3answers
687 views

is this language regular and why pumping lemma doesn't work?

I was told that this language is regular but as I can show below, pumping lemma is not working for it. What am I doing wrong? Is this language really regular? Why?
0
votes
1answer
86 views

Trying to simplify a particular regular expression

The question is as follows $$(a^* (ba)^* )^* (b+\epsilon) = (a+b)^* (b+\epsilon)\,.$$ But I am unable to solve this regex expression. My answer is as follows: \begin{alignat*}{2} (a^* + (ba)^* )^...
0
votes
2answers
75 views

Does there exists a finite automata for the given language?

The question is simple and given as, $alphabets=\{a, b\}$, and language $L$ over them as: $L = \{w: w \ € \{a, b\}^*, (n(a) - n(b)) \ mod \ 3=1\}$. Here $n(a)$ = number of $a$ and $n(b)$ is number of ...
1
vote
1answer
39 views

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

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
votes
1answer
83 views

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
vote
1answer
118 views

Can we prove using pumping lemma that language F = {$a^ i b ^j c ^k$ | i, j, k ≥ 0 and if i = 1 then j = k} is not regular?

I am currently solving a problem in which we have to show that we can not prove using pumping lemma that the language mentioned in the question is not regular.Here is the full question Consider the ...
3
votes
1answer
31 views

Given the regular set $S = a^*ba^*ba^*$, is the set $S'$ of all first thirds of strings in S (with length divisible by 3) regular?

I have no idea how to approach this problem, could I get at least a hint on how to go about proving/disproving this? I've tried the pumping lemma but I don't think it applies here. I've also tried ...
4
votes
1answer
96 views

Efficiently convert an NFA with multiple $\varepsilon$ edges and accepting states into a regular expression

Given an NFA with alphabet $\Sigma = \{a, b, c\}$ defined in the diagram, is there a way to efficiently convert it into a regular expression? The way I solved this problem is to first convert the NFA ...
6
votes
2answers
342 views

Find the language an NFA recognizes

For example, I have an NFA $A_n$ with alphabet $\Sigma = \{0, 1\}$. The language recognized by this NFA is known to be $\{u1v\ |\ u, v \in \Sigma^*, |v| = n − 1\}$. I was unable to get the ...
2
votes
2answers
90 views

Finding if the given language is regular or not

I have the language $$L = \{a^mb^nc^o| \, m + n + o > 5\}$$ where $m,n,o$ are non-negative integers. I have to find whether the language is regular or not. My attempt: I feel it should be non ...
0
votes
1answer
17 views

Choose the best classifier to predict the label of strings of a regular language

I have to tackle this problem: I have some strings that are my training set. These strings belong to a regular language corresponding to a deterministic finite automata (hidden namely I don't now it, ...
2
votes
1answer
36 views

Regular expression for capturing a “C-style” string

I have started to learn automata theory and languages. I am new to regular expressions. As a use case in real world, I would like to construct a regular expression to accept a c-style string: ...
1
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2answers
141 views

Is every regular/context free langauge decidable in LogSpace?

I know all the regular languages are decidable but not sure whether it can be done in LogSpace.
1
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1answer
71 views

Is the language $K=\{u \in\{0,1\}^n\mid n \geq 0, \forall_{v \in\{0,1\}^n} (u+v) \in L \}$ regular?

For two words $w,v \in\{0,1\}^*$ of equal length, let $w+v \in\{0,1,2\}^*$ denote the word in which the $i$-th word is the sum of $i$-th position of $w$ and $v$, as follows: if $w=a_1 \ldots a_n$ and $...
-1
votes
1answer
67 views

How to convert a CFL to a deterministic PDA?

I am trying to complete this question. However, I am unsure of the steps necessary to complete the conversion from a CFL to a deterministic PDA. I know that $ww' | w \in \left \{ a,b \right \}^{*}, w'...
3
votes
2answers
38 views

Question about mapping reducibility

I am working on an assignment where one of the sub questions is: Let $A$ and $B$ be languages. Suppose $A$ is context free and $A ≤_m B$, which means that there is a computable function $f\colon \...
3
votes
2answers
302 views

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
votes
3answers
2k views

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
vote
1answer
26 views

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 ...
4
votes
1answer
92 views

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
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1answer
54 views

Proof that (A ∪ B)∘C = A∘C ∪ B∘C where A, B and C are 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?
0
votes
1answer
49 views

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
votes
1answer
66 views

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
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1answer
35 views

Contradiction in regularity of a language

Lets say we have $L_1$ which contains all binary numbers divisivle by 2 but not by 4. I would say this language contains all words with a 10 at the end. Ive found a regular grammar $G$ with $L(G) = ...
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votes
2answers
94 views

Context free Grammar for this context free language

How can I create a context free grammar for the language $\{p^2q^mpr^nq^{2n+m}| m,n \ge 0\}$, where $\Sigma = \{p,q,r\}$?
2
votes
1answer
351 views

Determining if given languages are regular or recursively enumerable

I came across following problem: Suppose $L_1$ and $L_2$ are two languages, $M$ is a Turing machine $L_1 =\{M|M$ accepts at most 2016 strings$\}$ $L_2=\{M|M$ accepts at least 2016 strings$\}$ ...
2
votes
1answer
54 views

Is the language $a^nwa^n$ regular?

The given description of language is: $\Sigma=\{a,b\}$ and $L=\{a^nwa^n:n\geq 1,w\in\Sigma^*\}$ I felt its regular as we can always interpret $aabaa$ in string $aaabaaa$ as $w$. That is we can ...
0
votes
1answer
86 views

Generation regular languages by context free grammar

I came across problem asking whether given statement is true and false. The statement given was as follows: Every Type-2 grammar can generate regular language. I felt that Type-2 grammar means, ...
4
votes
2answers
80 views

Proving that $\{0^{m^2}\mid m\geq 3\}^*$ is regular

We know that $L=\{0^{m^2}\mid m\geq 3 \}$ is not a regular language. However $L^*$ is regular because we can generate $0^{120}$ to $0^{128}$ by some concatenations and then any other power of $0$ can ...
1
vote
1answer
29 views

Number of strings accepted by this regular expression

This was a question that I got while taking a test at our university. The question paper was taken away after the exams. I remember the question only, not the multiple choices. If a regular ...
0
votes
3answers
80 views

Concatenation of language to itself zero times

I was solving this question: Which of the following statement(s) is/are false? $L^0=\{\epsilon\}$ $|L^0|=0$ The answer given was None. That is, none of these statements are false and ...
1
vote
1answer
41 views

“Or” in regular expressions

I'm a bit new to automata theory, I'm sorry if this question is a bit too simple. If this question has been answered somewhere already, please point me to it. One basic problem I wanted to solve was ...
1
vote
1answer
350 views

Understanding facts about regular languages, finite sets and subsets of regular languages

I am aware of following two facts related to two concepts: regular languages and finite sets: Regular languages are not closed under subset and proper subset operations. It is decidable ...
1
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1answer
410 views

Difference between regular language and context free language

What is nature of difference of regular language and context free language? My guess is RL - CFL = RL CFL - RL = CFL Am I correct with this?
0
votes
0answers
61 views

Conversion from automaton to left linear grammar

I stumble across this problem: Give right linear grammar. The solution given was simple: $S\rightarrow bA$ $S\rightarrow aS$ $A\rightarrow \lambda$ $B\rightarrow bA$ $A\rightarrow aB$ Earlier ...
3
votes
1answer
435 views

Understanding application of Arden's theorem to find regular expression

I learnt Ardens theorem and its usage as follows: Ardens Theorem Let $P$ and $Q$ be two regular expressions over alphabet $Σ$. If $P$ does not contain null string, then $R = Q + RP$ has a ...
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1answer
32 views

Regularity under set difference

Let L be a regular language. Then $\Sigma^{*} \backslash L^{*} = (\Sigma^{*} \backslash L)^{*}$ How do I prove it is wrong?
7
votes
3answers
909 views

Why does the Pumping-lemma for context-free languages use uvwxy, but the one for regular ones uvw?

Basically what the title says. Why can you "ignore" the "xy" part if you want to prove whether a language is regular?
1
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1answer
24 views

Prove or disprove those languages are regular

in my practice for a test I came across this question: prove or disprove that those languages are regular: I succeeded proving that the second language is nonregular with homomorphism but i'm having ...
0
votes
0answers
76 views

Show that language is context-free

Let $A$ be a pushdown automata with input alphabet $\Sigma$ and stack alphabet $\Gamma$ and let $R \subseteq \Gamma^∗$ be a regular language. Let $L_R(A) \subseteq \Sigma^∗$ be a language of such ...
2
votes
1answer
65 views

Why is $L := \{b^2a^nb^ma^3|m,n \geq 0\}$ a regular language?

(Pre-note: I'm learning Theory of Computation on my own, so bear with me if I'm saying something wrong/stupid.) Why is $L := \{b^2a^nb^ma^3\mid m,n \geq 0\}$ a regular language? This question ...
1
vote
0answers
16 views

Pseudo-random regex-searchable function

Let $L$ be the set of strings of length $n$ (say $n=400$, for example). Let $N = \{0,1,\dots,|L|-1\}$. I am looking for a function $f : N \to L$ with the following properties: $f$ is efficiently ...
1
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1answer
33 views

Proving that Pre(L) is regular using automatas: Should I prove that Pre(L) is the semantic of the new automata?

Let $L$ be a regular language, and $Pre(L)$ be the set of all words that are prefix of some word in $L$. Prove that $Pre(L)$ is regular. My proof: Let $M = (\Sigma, Q, \delta, q_0, F)$ be an ...
8
votes
5answers
2k views

Finite state automata: final states

In our programming language concepts course, our instructor claimed that it's okay for a final state to lead to another state in a finite state diagram. But this seems to be a fundamentally ...
3
votes
1answer
185 views

This doesn't seem like a valid regular grammar; my instructor says it is

The following is a screenshot of a lecture slide from my programming language concepts course: According to Wikipedia and other sources, a regular grammar is one that is either left linear or right ...
1
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1answer
37 views

Determining whether $L^*$ is a finite union of $L^n$ for unary regular $L$

Give an algorithm that, given an NFA over a one-letter alphabet, determines whether the language it generates has the property that for some $n$, $$ L^* = \bigcup_{k=0}^n L^k. $$ I need some tips how ...
2
votes
1answer
43 views

unambiguous equivalent grammar

There is a grammar G given: S->XaX X->aX|bX|eps I just replied to the first question that was ...
1
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1answer
95 views

How to prove that a bounded pushdown automaton is regular?

I'm studying computer science and I want to show that a language which is accepted by a pushdown automaton with a bounded stack height is regular, but I'm totally lost... Can someone try to explain ...