Pick all true statements about REGEXs:

Question

BlackTom AI · Accepted Answer

Regular expressions (formal regular expressions) are syntactic expressions that denote sets of strings over an alphabet — i.e., they denote languages. A formal REGEX constructs languages using concatenation, alternation (union), and Kleene star; the class of languages it can describe is exactly the class of regular languages (those accepted by finite automata).

Step-by-step reasoning:
1. Definition and mapping: A REGEX is a formula whose semantics is “the set of all strings matching the formula.” Thus syntactically valid REGEXs always have a well-defined language (possibly the empty language ∅ or the language {ε} containing only the empty string). Therefore “Every REGEX represents a language” is true.
2. Scope of expressiveness: The class of languages representable by REGEXs is the regular languages. That means REGEXs represent some formal languages (all regular ones) but not all possible formal languages. Hence the statement “REGEXs are a more compact way to represent 'some' formal languages” is true: they compactly and declaratively describe regular languages (e.g., a*b* compactly represents {a^i b^j | i,j ≥ 0}) without listing infinitely many strings or explicitly building automata.
3. Counterexamples for universality: “Every language can be represented by a REGEX” is false because there exist non-regular languages, e.g., L = {a^n b^n | n ≥ 0}, which cannot be described by any regular expression (pumping lemma or closure properties show non-regularity).
4. “None is correct” is false because two of the provided statements are correct, as argued.

Why the correct answers are correct: the formal theory of computation proves the equivalence between regular expressions and finite automata (they denote exactly the regular languages), which justifies both true assertions above. The incorrect options fail because REGEXs cannot capture non-regular languages, and therefore not “every language,” and because at least two statements are indeed correct.

Final confirmation: the correct choices are “REGEXs are a more compact way to represent "some" formal languages.” and “Every REGEX represents a language.” These match the provided answer.

Pick all true statements about REGEXs:多项选择题

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What language does the following REGEX r represent? r = ( lam* )* Note: phi is used for 𝜙 , and lam is used for 𝜆

REGEX is a mathematical tool to represent "some formal languages".

REGEXs represent "some formal languages" in a more compact way.

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