Questions tagged [regular-expressions]

Questions about regular expressions, a formalism to describe regular languages.

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Quickly converting a regex into a minimized DFA

Is there some sort of algorithmic way to quickly convert a regex into a minimized DFA? I am able to somehow "guess" the DFA by playing around with the regex (as shown in the image, where the ...
98 views

Why $(a+b)^* = (a^*b)^* a^*$

I have seen on a book that for regular expressions it holds the equality $(a+b)^* = (a^*b)^* a^*$ but I am not seeing why. It is clear that the language generated by $(a+b)^*$ contains $(a^*b)^* a^*$, ...
1 vote
79 views

How to formally prove that any regular expression can be written as a finite combination of base cases and operations?

In Michael Sipser's book, "Introduction to the Theory of Computation," regular expressions are defined as follows: Based on this definition, how can I formally prove that any regular ...
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Construct a Regular Expression for Identifying strings containing '11' followed by an odd number of '0's

I need to construct a RE for identifying the string which contains 11 followed by an odd number of zero, this is in context for Compiler Design and then it needs to be converted into a NFA then to DFA....
25 views

Formal regular expression equivalent for this programming regex

Consider these Regexes written in Julia (they should be equivalent in Python): ...
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Is complement of this language context-free? [duplicate]

Let $L = \{wcw : w \in \{a, b\}^\ast\} \subseteq \{a, b, c\}^\ast$. From what I know, this language is not a context-free language but how about complement of this language? I know that the class of ...
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How is $|xy^{2}z| < 2^{p+1}$ (Pumping Lemma application)

In the Question here it is said that $|xy^2z|<2^{p+1}$ Considering that $|x| = 0$ and $|z| = 0$, y consists of $2^{p}$. It's probably trivial, but how do I see, that $|xy^2z| < 2^{p+1}$?
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590 views

What does empty string ε actually mean?

I came across this weird expression while learning about regular expressions. $R^+ \cup \varepsilon = R^*$ why does doing union with an empty string makes this regex go from 1 or more to 0 or more?
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2k views

Converting Regex to DFA

People I know said that converting a Regex to DFA is just a "matter of judgement" (I do not believe them, there has to be a more systematic approach). Is there a simple/intuitive, yet ...
74 views

How to work thompson's construction algorithm?

Could someone explain to me, through an example, how the McNaughton–Yamada–Thompson algorithm works in a way that I can understand? Thank you in advance for your helpful response!
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If a person accidentally deletes a few letters when they try to type "IDAHO" or "ILLIONOIS", then when is state name unclear or ambiguous?

The Short Version of my Question The following two regular expressions represent two sets of strings. REGEX EXAMPLES OF STRINGS OF TEXT THAT MATCH THE REGEX ...
36 views

Flex's NFA Determinization Algorithm

I am trying to understand how the algorithm used by Flex works. I refer to the determinization procedure producing the output DFA. The algorithm is publicly available and contained in Flex's source ...
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Formally Verify if a Sequence of Regex-Based Modifications is Idempotent

I'm performing a sequence of text formatting using regex in Python. I'm curious to know if it's possible to formally verify whether a single (or a sequence of) regex modification(s) is idempotent, ...
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How does a regular expression match .+x?

A quick test shows what I'm describing: > const text = 'foobarhelloworld' > const pattern = /.+or/ > text.match(pattern) //=> 'foobarhellowor' What is ...
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What is the minimum length word accepted by the product of these simple loop automata?

Let $A_{n} = (aa|aaa|aaaa|\dots |a^{n-2})(a^{n})^*$ where $n \geq 4$ is some natural,and $A_2 = (a^2)^*, A_3 = (a^3)^*$. Clearly every transition is thus labeled by an $a$. From now on let $A_n$ ...
242 views

Construct a regular grammar that produces all possible strings of $\Sigma = \{a,b\}$ that do not contain substring 'abba'

I'm really stuck here and do not know what to do. So far, I've constructed a DFA and a regular expression that produces the aforementioned set of strings. Namely, the DFA looks like: After a lot of ...
128 views

Is the language regular A2 = {w1w2w3 | w1, w2, w3 ϵ {0, 1}* }? How to prove?

So I think the above language is regular. I tried using pumping lemma but pumping up or down, changes the value of w1 but has no relation with w2 or w3. The resulting string after pumping will also be ...
49 views

Binary combinatorics with rank

I am looking at finding acceptable binary values with maximum 2 consecutive 1s and 0s, from a range of maximum 6 bits (2^6 values). Also, I want to rank and unrank these subset of values (in ...
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Regular expression for binary string containing no instances of 01

In order to enumerate such a regular expression, it's clear one can break down the language into the set $s =\{00,01,10,11\}$ and it is clear that we need to enumerate some expression that avoids the ...
1 vote
111 views

How to simplify this regular expression?

How do i prove that the regular expression $$a^*(ba^*)^*$$ is the same as $$(a+b)^*$$. Is there a way to prove this using regular expression identities?
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For each of the following languages, give a regular expression over {a, b}

$\{a^{2n}b^{n+k+1}a^k ∈ \{a, b\}^∗ \mid n \ge 0, k \ge 0\}$
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Prove the language $a^n b^m$ where $m$ is a multiple of $n$ is not regular

Consider the problem Show $L = \{ a^{n}b^{m}\mid m \text{ es múltiplo de } n \}$ is not regular. I attempted the following. Assume $L$ is regular. Then there is a natural number $p \geq 1$ such ...
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1 vote
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The language of chains with twice as many $a$s as $b$s is regular?

I am trying to understand the pumping lemma and its instrumentation to show a certain language is not regular. My first attempt was the following problem: Let $L$ be the language of all words that ...
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1 vote
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Meaning/veracity of "each state has [..] or two outgoing ϵ transitions" in Thompson's construction

The dragon book lists properties of an NFA N(r) created using Thompson's construction, in particular: Each state of N(r) other than the accepting state has either one outgoing transition on a symbol ...
503 views

Prove or disprove that two regular languages are equivalent

I have $L_1=\{b^*+b^*a(b+ab^*a)^*ab^*\}$ and $L_2=\{(b^*ab^*a)^*b^*\}$. I want to prove or disprove that they are equivalent. I have proved that $L_2\subseteq L_1$ and I tried to transform the second ...
1 vote
89 views

Regex to DFA - How do I implement parsing preferences in regex search?

I've tried a to implement a Regex to DFA converter, and it works, so far, but I don't understand how to implement "parsing preferences" in the DFA. A classic example is $a^*$. This regex is ...
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35 views

Why are ] and } not considered special characters?

Reading the manual for GNU grep, the special characters (with -E option) are .?*+{|()[\^\$. This is a somewhat pedantic question, but why are ...
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What algrorithm computes a mutally exclusive partitioning from two regulair expressions?

The Question A regular expression, such as AL+[EYI]+, represents a set of strings. ...
1 vote
25 views

Errors in examples of Vardi's paper "Linear Temporal Logic and Linear Dynamic Logic on Finite Traces"

The paper Linear Temporal Logic and Linear Dynamic Logic on Finite Traces has the following examples on page 4: Q1. (Update to Q1: solved. See the comment by DCTLib.) The first example says that the ...
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