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Questions and Answers
Which regular expression accurately represents the set of all strings that begin with a 1 and end with a 0?
Which regular expression accurately represents the set of all strings that begin with a 1 and end with a 0?
- 1Σ*0 (correct)
- 10*
- 0Σ*1
- 1*Σ0
The regular expression Σ*0101Σ* describes the set of strings containing at least the substring 0101.
The regular expression Σ*0101Σ* describes the set of strings containing at least the substring 0101.
True (A)
Write a regular expression for the set of strings w where w contains exactly two 1s.
Write a regular expression for the set of strings w where w contains exactly two 1s.
01010*
The regular expression for the set of strings where every odd position is a 1 is (1Σ)*(ε ∪ ______).
The regular expression for the set of strings where every odd position is a 1 is (1Σ)*(ε ∪ ______).
Match the following regular expressions with the sets of strings they represent:
Match the following regular expressions with the sets of strings they represent:
Which of the following statements is true regarding regular expressions and formal languages?
Which of the following statements is true regarding regular expressions and formal languages?
The Kleene Star closure includes the null string (^), while the Plus operation does not.
The Kleene Star closure includes the null string (^), while the Plus operation does not.
Describe the difference between Kleene Star closure and Plus operation, focusing on the strings they generate from the alphabet {b}.
Describe the difference between Kleene Star closure and Plus operation, focusing on the strings they generate from the alphabet {b}.
A regular expression is a pattern describing a certain amount of ______ of text.
A regular expression is a pattern describing a certain amount of ______ of text.
Match each operation with its equivalent expression using 'c'.
Match each operation with its equivalent expression using 'c'.
Given the alphabet {0}, which of the following regular expressions represents the language of all strings of zeros with at least one zero?
Given the alphabet {0}, which of the following regular expressions represents the language of all strings of zeros with at least one zero?
If L = {ab, bb}, then the language L* (Kleene Star of L) will not contain the string 'aba'
If L = {ab, bb}, then the language L* (Kleene Star of L) will not contain the string 'aba'
Provide two different regular expressions that could represent the language containing only the string 'hello'.
Provide two different regular expressions that could represent the language containing only the string 'hello'.
Which of the following regular expressions generates the language L = {a, aa, aaa, aaaa, ...}?
Which of the following regular expressions generates the language L = {a, aa, aaa, aaaa, ...}?
The regular expressions a* and a+ generate the exact same language.
The regular expressions a* and a+ generate the exact same language.
Write a regular expression for the language of all strings consisting of zero or more 'b's.
Write a regular expression for the language of all strings consisting of zero or more 'b's.
In regular expressions, the symbol + typically means one or more occurrences, while the symbol * means ________ occurrences.
In regular expressions, the symbol + typically means one or more occurrences, while the symbol * means ________ occurrences.
Which of the following regular expressions will generate any string of concatenation of 'a' and 'b'?
Which of the following regular expressions will generate any string of concatenation of 'a' and 'b'?
The regular expressions ab* and a(^ + b+) are equivalent.
The regular expressions ab* and a(^ + b+) are equivalent.
Write a regular expression for the language of all words having even number of 'a's.
Write a regular expression for the language of all words having even number of 'a's.
The regular expression a(aa)* generates words with ____ number of a's only.
The regular expression a(aa)* generates words with ____ number of a's only.
In C language, identifiers must start with a letter or an underscore. Given L denotes [a-z, A-Z] and D denotes [0-9], which regular expression represents a valid identifier?
In C language, identifiers must start with a letter or an underscore. Given L denotes [a-z, A-Z] and D denotes [0-9], which regular expression represents a valid identifier?
Match each regular expression with the language it generates:
Match each regular expression with the language it generates:
Flashcards
Arithmetic Operators
Arithmetic Operators
Basic mathematical operations: +, -, *, /, %
Logical Operators
Logical Operators
Operators that perform logical operations: &&, ||, !
Increment/Decrement Operators
Increment/Decrement Operators
Operators that increase or decrease a value by 1: ++, --
Relational Operators
Relational Operators
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Regular Expressions for Strings
Regular Expressions for Strings
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Regular Expression
Regular Expression
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Regular Language
Regular Language
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Non-Regular Language
Non-Regular Language
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Kleene Star Closure
Kleene Star Closure
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Plus Operation
Plus Operation
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Positive Closure
Positive Closure
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Kleene Star vs. Plus
Kleene Star vs. Plus
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Positive Closure Relationship
Positive Closure Relationship
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Regular Expressions (RE)
Regular Expressions (RE)
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Kleene Star (*)
Kleene Star (*)
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Kleene Plus (+)
Kleene Plus (+)
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a*
a*
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a+
a+
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(r1) r2
(r1) r2
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(L | _) (L | _ | D)*
(L | _) (L | _ | D)*
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(aa)*
(aa)*
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a(aa)*
a(aa)*
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(r1 + r2)
(r1 + r2)
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Study Notes
Regular Expressions
- Regular expressions (RE) are used to precisely define formal languages, making them more understandable than lengthy descriptions.
- They resemble arithmetic expressions, but have distinct characteristics.
- Not all formal languages can be described by regular expressions. Those that can are called "regular languages," others are "non-regular."
- A given language might have multiple equivalent regular expressions.
Kleene Star Closure
a*represents zero or more occurrences of 'a' (including the empty string).a* = {^, a, aa, aaa, ...}- Kleene Star can be applied to any symbol or string.
Plus Operation (+)
a+represents one or more occurrences of 'a' (excluding the empty string).a+ = {a, aa, aaa, ...}- The difference from Kleene star is the absence of the empty string.
Relationships between Kleene Star and Positive Closure
a* = ^ + a+(The empty string plus one or more occurrences)a+ = a a*(One 'a' followed by zero or more occurrences)
Recursive Definition of Regular Expressions
- Every letter (including the empty string "^") in the alphabet (Σ) is a regular expression.
- If
r1andr2are regular expressions, then:r1 r2(concatenation)r1 + r2(union/alternative)r1*(Kleene star closure)
- Nothing else is a regular expression.
Examples of Regular Languages
-
{^, x, xx, xxx, ...}over Σ={x}:x* -
{x, xx, xxx, ...}over Σ={x}:x+ -
Important distinction between:
r1 = a*+b*andr2 = (a+b)*(The difference involves strings with mixing of a's and b's) -
Example: All words with one 'a' followed by any number of 'b's:
a b*ora(b*)ora(^+b+)
Regular Expressions for Identifiers and Operators
-
Identifiers (e.g., variable names in C): Must start with a letter or underscore, followed by any combination of letters, digits, or underscores.
- Regular expression:
(L | _ ) (L | _ | D)*(where L=[a-zA-Z], D=[0-9])
- Regular expression:
-
Operators (various C operators): (Examples of various operators are given in the text, as well as examples of how to express them with regex) Examples include Arithmetic, Assignments, Increments/Decrements, Logical, Relational
More Examples/Use-cases for Regex
- The text provides numerous examples (and solutions) showing how regular expressions can describe specific patterns in strings (e.g. minimum/maximum lengths, specific symbols, etc.)
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Description
Learn about regular expressions and the Kleene star and plus operations. Regular expressions define formal languages and the Kleene star represents zero or more occurrences of a symbol, while the plus operation indicates one or more occurrences.
