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.
Questions tagged [regular-language]
1275 questions
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Is the set of all valid C++ programs countably infinite?
I have heard that the set of valid programs in a certain programming language is countably infinite. For instance, the set of all valid C++ programs is countably infinite.
I don't understand why though. A programming language has open curly braces…
John Hoffman
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4 answers
Can a regular grammar be ambiguous?
An ambiguous grammar is a context-free grammar for which there exists a string that has more than one leftmost derivation, while an unambiguous grammar is a context-free grammar for which every valid string has a unique leftmost derivation.
A…
Arman Malekzadeh
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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:
$half(L) = \{u \mid uv \in L\ s.t. |u|=|v|\}$.
Prove that if $L$ is regular then $half(L)$ is…
Aviad
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Mystery Men Movie - Propositional Logic
In the movie Mystery Men, there is this scene:
Captain Amazing (good guy): I knew you couldn't change.
Casanova Frankenstein (bad guy): I knew you'd know that.
Captain Amazing: Oh, I know. And I knew you'd know I'd know you knew.
Casanova…
LateralFractal
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11
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pumping lemma: ww^R not regular
I'm trying to prove that $L = \{ww^R : w \in \{a,b\}^*\}$ ($w^R$ is the reverse of $w$) is not regular using the pumping lemma.
Let $p$ be the pumping length and $s = a^pbba^p$.
$x = \epsilon$, $y = a^p$, $z = bba^p \implies s = \epsilon a^p bba^p =…
11
votes
6 answers
A computer's memory is finite, so how can there be languages more powerful than regular?
A computer has a finite memory. There are no computers with infinite memory. Therefore the only languages that a computer can process are those whose member strings are finite. As I recall, the computational power required for any finite language is…
Roger Costello
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10
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3 answers
Formally prove that every finite language is regular
I know how to prove this informally, but don't know what the formal proof should look like.
zeqof
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Converting to Chomsky Normal Form
I am trying to learn how to convert any context free grammar to Chomsky Normal Form. In the example below, I tried to apply Chomsky Normal Form logic, to result in a grammar, where every symbol either produces two symbols, or every symbol produces a…
AnchovyLegend
- 605
9
votes
1 answer
Is the set of regular languages closed under set difference?
Let $\Sigma$ be an alphabet and $L_1,L_2 \subseteq \Sigma^*$ two regular languages.
I know that $REG$ is closed under intersections of regular languages and under complementation of a regular language. My reasoning looks like this:
$L_1 \setminus…
Ștefan
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votes
4 answers
Intersection of two deterministic finite automata?
I'm trying to solve a problem where I have to create a DFA for the intersection of two languages.
These are:
$$\{s \in \{{\tt a}, {\tt b},{\tt c}\}^\ast : \mbox{every ${\tt a}$ in $s$ is immediately followed by a ${\tt b}$}\}$$
and
$$\{s \in…
AkshaiShah
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Prove regular language closed under min and max
Given some regular language $L$, show that $L$ is closed under the following operations:
$$\begin{align*}
\min(L) &= \{w\mid w\in L,\text{ but no prefix of }w\text{ is in }L \}\\
\max(L) &= \{w\mid w\in L,\text{ but for no }x\text{ other than…
user93189
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What is the probability that a random regular expression defines the language of all binary strings $\{0, 1\}^*$?
Suppose we generate a random regular expression $R$ in the following way:
We start with a single meta-symbol $S$. Then each turn we independently replace all $S$ in our word with $\{0\}$, $\{1\}$, $(S \cup S)$, $SS$ or $S^*$ with equal probability.…
Chain Markov
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If $L$ is regular, prove that $\sqrt{L}=\left\{ w : ww\in L\right\}$ is regular
Let $L$ be a regular language. Prove that $\sqrt{L}:=\left\{ w : ww\in L\right\}$ is also a regular language.
I suppose I need to modify state machine for $L$ to accept $\sqrt{L}$, but I've been thinking how to do that for a few hours and still…
xan
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NFA of $k$ states recognizing all words of length $\le k$
Let $N$ be an NFA with $k$ states that recognizes some language $A$.
a. Show that if $A$ is nonempty, $A$ contains some string of length at most $k$.
b. Show, by giving an example, that part (a) is not necessarily true if you replace both $A$’s by…
Artyom Dmitriev
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Why isn't this a regular language?
I'm stuck as to figuring out why $L_1$={$n^p$ | $p$ = a prime number} is not a regular language but $L_2$={$n^p$ | $p$ = a prime number bounded by some fixed number f} is. I can see that $L_2$ is a finite language so it's a regular language. But I…
pauliwago
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