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

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Showing that $\{ c^n a^m b^{n+m} : n+m \geq 6\}$ is not regular

I'm trying to show that $L_6=\{c^n a^m b^p : n+m=p,p \geq 6\}$ is not regular. I need a little help, I was practicing the pumping lemma, and I encountered this language, I saw these conditions and got ...
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2answers
35 views

How to prove that these two languages are regular, or not regular?

I have these two languages $L_1={\{a^n b^m,n≥m+5,m>0}\}$ Where $∑=(a,b)$ $L_2={\{a^n b^m,n≥m+5,m≤5}\}$ Where $∑=(a,b)$ As you can see that there is only one difference, the condition of ...
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1answer
23 views

Proving that any CF language over a 1 letter alphabet is regular

I would like to prove that any context free language over a 1 letter alphabet is regular. I understand there is Parikh's theorem but I want to prove this using the work I have done so far: Let L be a ...
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2answers
35 views

How can I see which language type will result from the union or intersection of different language types?

I have to decide which language type will result from the union of a type-2 (context-free) and a type-3 (regular) language. Is there a way or rule to decide this for all language types?
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1answer
86 views

Possessive Kleene star operator

Has anyone studied the consequences of the Kleene star in regular expressions to always be "possessive"? In other words, if * would always match as much as ...
2
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1answer
79 views

Why is $\{a^n b^m c^p: n\neq m\} \cup \{a^n b^m c^p: m\neq p\}$ an inherently ambiguous language?

I came across a very hard interview question in last month’s Ph.D. entrance exam. It was asking which one of the languages is inherently ambiguous. Short answer says 2). Why is the language in 2) an ...
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1answer
59 views

Prove A² is regular [duplicate]

Suppose that $A$ is a regular language. How can I show that $A^2 = A \cdot A$ is a regular language? Is there a construction?
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29 views

Kleene star property: proving $(A^+)^* = A^*$ [duplicate]

I should prove that $(A^+)^* = A^*$ in a very formal way, any hints?
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43 views

regular expression of star-height 1

Is there a regular expression of star-height 1 (i.e. without two nested Kleene stars) for the following language : $a^*(bb^*aa^*ba^*)^*$ ?
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0answers
23 views

Number of states of finite automata [duplicate]

Prove that for each $n>0$, a language $L_n$ exists where $L_n$ is recognizable by an NFA that has $n$ states, and If $L_n=K_1 \cup \dots \cup K_k$, for regular languages $K_i$, then at least ...
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0answers
12 views

Show that the language is regular [duplicate]

Let $L=\{k |km \in K \text{ for some } m \in M\}$. How can we show that if $K$ is regular and $M$ is any language, then $L$ is regular??
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2answers
59 views

Are regular languages closed against an intersection that keeps words with the same number of ones?

How can we show that the class of regular languages is closed under the following operation? Let $L_1$ and $L_2$ be laguages over $\Sigma=\{0, 1\}$. The operation is: $$\{x \in L_1 \mid \text{ for ...
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0answers
84 views

DFA for a regular language

I have a regular language consisting of such {0,1}^k sequences, in which every subsequence of length 5 has at least two 0's in ...
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2answers
73 views

Intersection of a language with a regular language imply context free

Lets say you have a language $L$ and you want to determine if it is context free. Context free languages intersected with regular languages are context free. Is that enough to prove that $L$ is ...
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1answer
35 views

designing a DFA and the reverse of it

There is a theorem that says if a language is regular, it's reverse is regular as well. How can I draw a DFA that shows if a language is regular, it's regular as well?
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1answer
37 views

What kind of subset any class of languages may or may not have?

There are different class of languages, regular,CFL, recursive and r.e. and non-r.e. Clearly a language is set of strings. if an infinite set belongs to any of these classes then what can we say about ...
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1answer
56 views

Is this language regular or non-regular: {ww : w ∈ {a,b}* } [duplicate]

This is a question from a text book that's giving me some trouble. The question is: Determine whether or not this language is regular. Justify your answer. $$L = \{ww : w \in \{a,b\}^* \}$$ I ...
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1answer
34 views

How do you prove two languages are equivalent using the definition of acceptance?

I need to prove that $L(f(M)) = L(M)\cup \{\varepsilon\}$ where $M$ is a DFA and $f$ is the function $f(M) := (Q\cup \{q_f\}, \Sigma, \delta', q_f, F\cup\{q_f\})$ and $q_f$ is a new state not in $Q$ ...
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1answer
141 views

How does a regular language satisfies the second condition of the pumping lemma

I'm a little bit confused about the second condition of the pumping lemma which are: $|y|\geq1$ $|xy|\leq p$ $\forall i \geq 0:xyiz\in L$ I don't understand why the length of ...
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1answer
33 views

Generate Regular Grammar for a Language with Modular Condition

This is a homework problem. I've wrestled with it for quite awhile and can't come up with a valid solution. The problem is: Find a regular grammar that generates each of the following languages: ...
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1answer
69 views

If L1 ∪ L2 and L1 are regular, is L2 also regular?

This is a problem in a theory of computation book that's stumping me: Suppose that we know that $L_1 ∪ L_2$ and $L_1$ are regular. Can we conclude that $L_2$ is regular? Explain. At first, I ...
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2answers
20 views

Prove that a language is not regular with process of elimination [duplicate]

When deterministic automaton, I need to prove that you can't implement the language in it, because the language is not regular. Easiest way to prove that a language is regular, is just by making an ...
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0answers
24 views

How these languages are context free and regular [duplicate]

I found these statements in my textbook without proof. If L is a Context Free Language over a one symbol alphabet then L is regular. Is there no context free language on one symbol ...
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1answer
44 views

Pumping Lemma confusion

I have the following language... $$A=\{a^ib^i | i>0\}\cup\{a^jb^k|j>2, k>3\}$$ Now, pumping lemma states that a regular language can be written in the form $x=pq^ir$. What confuses me is ...
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1answer
64 views

An example of a non-regular grammar for a regular language?

I understand that a regular language can be specified by either regular or non-regular grammars. What is an example of a non-regular grammar for a regular language?
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1answer
42 views

Pumping Lemma for Regular Language seems to Fail

Let $L = \{ab^ncd \mid n \geq 0\}$. If we take $p = 5$ and $w = abbcd$ and write $w_i = xy^iz$, where $x = abb$, $y=c$, $z=d$, then $w_2 = abbccd$ which is not in $L$. We conclude that ...
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1answer
34 views

Closure properties between 2 languages of different types [duplicate]

Whenever said - The intersection between a Context Free Language and a Regular Language is always Context Free, what is the best logical way to confirm the statement? I have this Chomsky hierarchy in ...
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1answer
84 views

Relaxation of the null production restriction in Regular and Context Free Grammars

I am convinced of the fact that allowing productions of the form $S \rightarrow \epsilon$ in a context sensitive grammar would allow RE languages to be expressed if $S$ were on the right hand side of ...
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0answers
25 views

What is the procedure for converting this finite automaton into a regular expression? [duplicate]

Could someone provide an explanation of how to convert this DFA into a regular expression? I have found three methods online, ie: How to convert finite automata to regular expressions? but they are ...
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1answer
96 views

What is meant by the notation $L(…)$?

I am currently studying about formal languages and automata. I am trying to solve a problem but there is a notation whose meaning I'm not sure of. I have a question to find out the relationship ...
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65 views

How do I show that a^n w b^n is not regular?

$\ \sum= \{a,b\} $ Show that: $ L:= \{a^nwb^n: m,n \in \mathbb N, m\geqslant n, w\in\sum^m\} $ is not regular. I'm trying to proof this with the Pumping Lemma, but I'm kind of confused because of the ...
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1answer
59 views

closure property on languages

The above image, taken from planetmath.org, describes the closure property on REG (regular), DCFL (deterministic context-free), CFL (context-free), CSL (context-sensitive), RC (recursive), RE ...
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1answer
55 views

Understanding Regular Grammers

I know a regular language is the one which can be expressed as a regular expression or we can create a DFA corresponding to it. Unless a language has a pattern in which one part has to match with ...
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1answer
54 views

Union of finite and non-regular language [duplicate]

Question: ($B$ and $C$ are languages) $B$ is finite,$C$ isn't regular: Prove/Disprove: $C\cup B$ isn't regular. Thoughts: My intuition says this is true, but I need an idea to prove it. Since I ...
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1answer
55 views

Three languages and how to decide if they are regular [closed]

From following languages which one is regular and why others are not?And what is the regular expression for regular one. $L_1= \{wxwy | x,y,w \in (a+b)^+\}$ $L_2 = \{xwyw | x,y,w \in (a+b)^+\}$ ...
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1answer
53 views

Is it Regular Language?

According to Wikipedia, Regular Language is Recognized by Some DFAs, or expressed by Regular Expression .. and all finite Language are regular but, not all regular is finite .. that's mean it may be ...
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1answer
56 views

Create CFG and pushdown automaton for {ww} [duplicate]

I've been trying to make a CFG, a pushdown automaton and a regular expression for the language $\qquad L(M) = \{ww : w \in \{a, b\}^*, |w| \text{ is even}\}$. I understand how the reverse of the ...
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63 views

L ={ $a^{m^n}$ | $m$>$n$ } is Regular or not by pumping Lemma [duplicate]

L ={ $a^{m^n}$ | $m$>$n$ } I am bit confuse whether to consider this language as L = $(a^{m})^{n}$ OR L = $a^{\left(m^n\right)}$. If it is considered as L = $(a^m)^{n}$ then want to check it ...
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2answers
33 views

Automaton accepting $\{a^{2i}bc^{2k} \mid i, k \in\mathbb{N}\}$

How can I produce an automaton accepting $\{a^{2i}bc^{2k} \mid i, k \in\mathbb{N}\}$? I am essentially confused about exactly what the $2i$ and $2k$ mean. Does that mean that the automaton only ...
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2answers
41 views

Intersection of regular and not regular

$L_1=\{a^n\mid n\ge1\}$ is regular and $L_2=\{a^{n^2}\mid n\ge1\}$ is non-regular. We know that $L_1\cap L_2$ is regular but, here $L_1\cap L_2=L_2$; and $L_2$ is not regular. How is this possible?
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Kleene closure, concatenation problem

If $L_1 = \emptyset$ , $L_2= \{a\}$ then what is $$L_1\cdot L_2^* \cup L_1^*$$ The answer given is $\{\epsilon\}$ but I think it should be $\{\epsilon,a\}$. My Approach : $L_1^* = \{\epsilon\}$ ...
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3answers
101 views

Was there an attempt to make reusable regular expressions?

In everyday practice I often encounter tasks which would benefit from being able to define aliases for chunks of regular expressions to reuse them later. Typical examples include: parsing a floating ...
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context free grammar to NFA

I've been given an exercise to solve which goes as follows: generate an NFA from the given CFG, $$\begin{align*}S &\to AB \mid c\\ A &\to aAb \mid c\\ B &\to bBa \mid c\ . \end{align*}$$ ...
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1answer
41 views

Give an example of a non-regular language $L$ such that $L^*$ is regular [duplicate]

I can't think of an example of a non-regular language $L$ such that $L^*$ is regular. . Any help ?
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1answer
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Language of binary strings divisible by 7

There was a question something like, "Consider the language of all integers converted to binary form. The language of all strings divisible by 7 is : 1) Recognizable by a finite-automaton. 2) ...
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1answer
23 views

Automata for languages derived from an automaton by number of state visits

My question in response to this answer: what would the finite automata look like for $L_1$ and $L_0$ in the answer? I get how the languages are formed; however, since $M_L$ cannot remember how many ...
2
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1answer
69 views

Finite Automata — Determine if a set is regular

I have been at this for hours. The question is: Prove that the language $A = \{0^kx \mid k > 0, x \in \{0,1\}^*, \text{ and } \#(0,x) \geq k\}$ is regular, where $\#(n, x)$ denotes the ...
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1answer
124 views

are regular languages closed under division

I am trying to solve this question which appeared in previous exam paper Can someone help me what i am failing to understand For languages $A$ and $B$ define $A \div B = \{x \in \Sigma^{\ast} : xy ...
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1answer
106 views

regular expression for binary language has at least one 1

So I had an exam in the subject "Theory Of Computation" and one of the questions was to write down a regular expression of a binary language that has at least one (1) , my answer was : 0* 1 0* (0* 1 ...
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1answer
61 views

How to prove that the Myhill-Nerode equivalence classes for L are the same as for its complement?

Given language $L$, I want to show that its Myhill-Nerode equivalence classes are the same as for its complement $\overline{L}$. I am thinking of constructing a DFA $M$ for the Language $L$ so the ...