题目

COMP30026_2025_SM2 Worksheet 7

多重下拉选择题

Complete the following statements about the languages given, over the alphabet Σ={b, e}: Let R = eb(ebb)(ε ∪ e), which is all strings that do not contain “bee”. The language A = L(R) is [ Select ] regular, R is not a correct regular expression not regular, R is not a correct regular expression regular, R is a correct regular expression not regular, R is a correct regular expression . Let B = {bee}. The language B is [ Select ] not regular regular . The language D = {w∈Σ* | w contains the substring bee exactly once} is [ Select ] regular, because D = A◦B◦A and regular languages are closed under concatenation unknown, because D = A◦B◦A, where one of the languages is not regular not regular, because D = A∪B, where one of the languages is not regular regular, because D = A∪B and regular languages are closed under concatenation unknown, because D = A∪B, where one of the languages is not regular not regular, because D = A◦B◦A, where one of the languages is not regular . The language K = {w∈Σ* | w contains n occurrences of the substring bee, where n≥1} is [ Select ] (D◦A◦B)* D* D∪B D\A DD , and is therefore [ Select ] unknown because at least one of the languages isn’t regular not regular because regular languages aren't closed under Kleene star not regular because at least one of the languages isn’t regular regular because regular languages are closed under concatenation and Kleene star regular because the regular languages are closed under union not regular because the regular languages aren’t closed under concatenation .

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Question restatement and options: - We are given R = e*b*(ebb*)*(ε ∪ e) over Σ = {b, e}, and A = L(R) is ______; B = {bee} is ______; D = { w ∈ Σ* | w contains the substring bee exactly once } is ______; K = { w ∈ Σ* | w contains n occurrences of the substring bee, where n ≥ 1 } is ______, and then K is ______. Option-by-option analysis for each part: First part (A): 'A = L(R) is' - Option: 'regular, R is a correct regular expression' (the provided correct choice in the list). Analysis: The language described by R consists of all strings over {b,e} that do not contain the substring 'bee'. The given expression R = e*b*(ebb*)*(ε ∪ e) is a standard regular expression that generates exactly those strings by allowing any number of leading e's, then any number of b's, then a block structure (ebb*)* to prevent the forbidden pattern, and ending with either ε or an e. This matches the idea that the language is regular (regular expressions characterize regular languages), and R is indeed a valid regular expression for A. Therefore this option is correct for this part. - Option: 'regular, R is not a correct regular expression' Reasoning: This contradicts the explicit construction; since R is a formal regular expression that generates strings without 'bee', it i......Login to view full explanation