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Skip to main content \(\renewcommand{\chaptermark}[1]{\markboth{#1}{}} \renewcommand{\notesname}{} \newcommand{\authormasthead}{ \begin{flushleft} \rule{0.3\linewidth}{0.3mm} \lettrine[lines=2]{J}{ournal of Inquiry-Based Learning in Mathematics} \rule{0.3\linewidth}{0.3mm} \end{flushleft} } \renewcommand{\enotesize}{\normalsize} \newcommand{\timestamp}{{Edited: \texttt{\now , \today}}} \renewcommand{\headrulewidth}{0.4pt} \renewcommand{\footrulewidth}{0.4pt} \newcommand{\InstructorVersion}{\includecomment{annotation}} \newcommand{\StudentVersion}{\excludecomment{annotation}} \newcommand{\nin}{} \newcommand{\msk}{} \newcommand{\bsk}{} \newcommand{\gsk}{\giantskip} \newcommand{\ra}{\rightarrow} \newcommand{\el}{\mathcal L} \newcommand{\ps}{\mathcal P} \newcommand{\ba}{\mathbf a} \newcommand{\bb}{\mathbf b} \newcommand{\bc}{\mathbf c} \newcommand{\bd}{\mathbf d} \newcommand{\be}{\math...

Given an alphabet Σ , recall that a regular language R is a certain subset of the free monoid M generated by Σ , which can be obtained by taking singleton subsets of Σ , and perform, in a finite number of steps, any of the three basic operations : taking union, string concatenation, and the Kleene star . The construction of a set like R is still possible without M being finitely generated free. Let M be a monoid, and 𝒮 M the set of all singleton subsets of M . Consider the closure ℛ M of S under the operations of union, product , and the formation of a submonoid of M . In other words, ℛ M is the smallest subset of M such that • ∅ ∈ ℛ M , • A , B ∈ ℛ M imply A ∪ B ∈ ℛ M , • A , B ∈ ℛ M imply A ⁢ B ∈ ℛ M , where A ⁢ B = { a ⁢ b ∣ a ∈ A , b ∈ B } , • A ∈ ℛ M implies A * ∈ ℛ M , where A * is the submonoid generated by A . Definition . A rational set ...

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Jump to content Main menu Main menu move to sidebar hide Navigation Main page Contents Current events Random article About Wikipedia Contact us Donate Contribute Help Learn to edit Community portal Recent changes Upload file Languages Language links are at the top of the page across from the title. Search Search Create account Log in Personal tools Create account Log in Pages for logged out editors learn more Contributions Talk CentralNotice move to sidebar hide (Top) 1 See also 2 References Toggle the table of contents Toggle the table of contents Atlantic City algorithm 3 languages Español Français עברית Edit links Article Talk English Read Edit View history Tools T...

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