# Tagged Questions

Regular languages are formal languages which are recognized by a finite automaton. It is equivalently the languages which are expressible as a regular expression. In addition to these two, there are several other equivalent definitions.

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### Converting Automata To Regular Expression Using State Removal Method

From the following automaton this solution is given: $$(a\mid b)^*aa(ba)^*a(a\mid b)^*$$ But when I try to convert this automaton into a regular expression I always end up with the wrong ...
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### How to prove non-regularity of a language from the non-regularity of another language?

How can I prove that $L_1=\{a^nb^m\mid n\ne m\}$ is not regular based on the fact that the language $L_2=\{a^nb^n\mid n\in\Bbb N\}$ is not regular? Thank you
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### How to prove that a simple NFA is minimal, without any algorithm?

First, I will present the question I was doing: We will define $p(L)$ to be the minimal natural number so that a language L fulfill the pumping lemma. We will also define $n(L)$ to be the minimal NFA ...
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### Do the initial segments of the strings of a regular language form a regular language?

Let's say you have a set of strings $R$. A string $s$ is part of my language $S$ iff there is a string $r \in R$ such that $s$ is an initial segment of $r$ (you can get $s$ by removing characters from ...
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### Is the resulting language regular?

If $L$ is a regular language then is $L'=\{w \mid wx \in L \text{ for some string }x\}$ regular? First step is understand $L'$. So it is a subset of $L$ that contains strings with a certain prefix?
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### Cocke-Younger-Kasami (CYK) Proving a word is in a language

Using CYK algorithm I need to figure out whether the word abbabb is a word of the language of the following grammar. I think I have completed the problem correctly but I'm not sure, I'm hoping ...
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### What does arbitrary number mean?

A FSM (Finite State Machine) can be designed to add two integers of any arbitrary length (arbitrary number of digits). Is it true ? My attempt : Arbitrary length means variable length, and there ...
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### Identify the class of language?

Given a set $$S=\{x∣ \text{there is an x-block of 5's in the decimal expansion of π}\}$$ (Note: x-block is a maximal block of x successive 5's). Identify class of language? Somewhere it ...
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### Proving that the language $\{w\in \{a,b\}^* \big|\#_a(w)< \#_b (w)\}$ is non regular using the pumping lemma

I need to prove that the language $\mathscr L=\{w\in \{a,b\}^* \big|\#_a(w)< \#_b (w)\}$ is non regular using the pumping lemma My try: $\{a,b\}^*=\{\epsilon,a,b,aa,ab,ba,bb,aaa,aab,\dots\}$ ...
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### Read-only Turing machine recognizes only regular languages?

Show that the Turing machines, which have a read only input tape and constant size work tape, recognize precisely the class of regular languages. According to wiki : A read-only Turing machine or ...
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### Writing a regular expertion for the language $L=\{0^n1^m \mid n\equiv m\pmod 2\}$

I need to write a regular expertion for the language of all the binary words that contains continuum of even number of zeros and after that even number of ones or odd number of zeros and after that ...
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### Language of all the binary words that not contains continuum of more then $3$ zeros

I need to write a regular expertion for the language of all the binary words that not contains continuum of more then $3$ zeros, for example $0011110100\in L,\,\,\,\,\,\,\,\,\,11000001100\notin L$ ...
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### $L=\left\{ s \in (0+1)^* \mid \text{ for every prefix s' of s,} \mid n_{0}(s')-n_{1}(s') \mid \leq 2 \right \}$ is regular?

Given language : $L=\left\{ s \in (0+1)^* \mid \text{ for every prefix s' of s,} \mid n_{0}(s')-n_{1}(s') \mid \leq 2 \right \}$ is regular? Somewhere it explained as : Here we need just 6 states ...
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### Proof of L being a regular languaje

I have the following language $$L = \{w\in\{a,\;b\}^* : a^nv,\; n\geq 1 \wedge |v|_a \geq n\}$$ Formed by characters "$a$" and "$b$" where the word $v$ has more "$a$" characters than $a^n$. I have ...
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### Automata | Prove that if $L$ is regular than $half(L)$ is regular too

I've see couple of approaches to this kind of questions yet I have no clue how to approach this one. Let L be regular language, and let half(L) be: $half(L) = \{u | uv \in L\ s.t. |u|=|v|\}$ Prove ...