6 \contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.14}

     6 \contentsline {chapter}{\numberline {1}POSIX Lexing With Bit-codes}{1}{chapter.14}

     7 \contentsline {section}{\numberline {1.1}Why Brzozowski}{2}{section.15}

     7 \contentsline {section}{\numberline {1.1}Introduction To Regexes}{1}{section.15}

     8 \contentsline {section}{\numberline {1.2}Backgound}{4}{section.16}

     8 \contentsline {subsection}{\numberline {1.1.1}Back References in Regex--Non-Regular part}{4}{subsection.16}

     9 \contentsline {section}{\numberline {1.3}Existing Practical Approaches}{5}{section.17}

     9 \contentsline {section}{\numberline {1.2}Our Solution--Brzozowski Derivatives}{4}{section.17}

    10 \contentsline {subsection}{\numberline {1.3.1}DFA Approach}{5}{subsection.18}

    10 \contentsline {section}{\numberline {1.3}Preliminaries about Lexing Using Brzozowski derivatives}{4}{section.18}

    11 \contentsline {subsection}{\numberline {1.3.2}NFA Approach}{5}{subsection.19}

    11 \contentsline {section}{\numberline {1.4}Backgound}{14}{section.25}

    12 \contentsline {section}{\numberline {1.4}Our Approach}{5}{section.20}

    12 \contentsline {section}{\numberline {1.5}Engineering and Academic Approaches to Deal with Catastrophic Backtracking}{15}{section.26}

    13 \contentsline {subsection}{\numberline {1.4.1}Existing Work}{5}{subsection.21}

    13 \contentsline {subsection}{\numberline {1.5.1}DFA Approach}{15}{subsection.27}

    14 \contentsline {section}{\numberline {1.5}What this Template Includes}{5}{section.22}

    14 \contentsline {subsection}{\numberline {1.5.2}NFA Approach}{15}{subsection.28}

    15 \contentsline {subsection}{\numberline {1.5.1}Folders}{5}{subsection.23}

    15 \contentsline {section}{\numberline {1.6}Our Approach}{15}{section.29}

    16 \contentsline {subsection}{\numberline {1.5.2}Files}{6}{subsection.24}

    16 \contentsline {subsection}{\numberline {1.6.1}Existing Work}{15}{subsection.30}

    17 \contentsline {section}{\numberline {1.6}Filling in Your Information in the \texttt {\bfseries main.tex} File}{7}{section.25}

    17 \contentsline {section}{\numberline {1.7}What this Template Includes}{16}{section.31}

    18 \contentsline {section}{\numberline {1.7}The \texttt {main.tex} File Explained}{7}{section.26}

    18 \contentsline {subsection}{\numberline {1.7.1}Folders}{16}{subsection.32}

    19 \contentsline {section}{\numberline {1.8}Thesis Features and Conventions}{8}{section.27}

    19 \contentsline {subsection}{\numberline {1.7.2}Files}{16}{subsection.33}

    20 \contentsline {subsection}{\numberline {1.8.1}Printing Format}{8}{subsection.28}

    20 \contentsline {section}{\numberline {1.8}Filling in Your Information in the \texttt {\bfseries main.tex} File}{17}{section.34}

    21 \contentsline {subsection}{\numberline {1.8.2}Using US Letter Paper}{9}{subsection.29}

    21 \contentsline {section}{\numberline {1.9}The \texttt {main.tex} File Explained}{17}{section.35}

    22 \contentsline {subsection}{\numberline {1.8.3}References}{9}{subsection.30}

    22 \contentsline {section}{\numberline {1.10}Thesis Features and Conventions}{18}{section.36}

    23 \contentsline {subsubsection}{A Note on bibtex}{9}{section*.32}

    23 \contentsline {subsection}{\numberline {1.10.1}Printing Format}{19}{subsection.37}

    24 \contentsline {subsection}{\numberline {1.8.4}Tables}{10}{subsection.33}

    24 \contentsline {subsection}{\numberline {1.10.2}Using US Letter Paper}{19}{subsection.38}

    25 \contentsline {subsection}{\numberline {1.8.5}Figures}{10}{subsection.35}

    25 \contentsline {subsection}{\numberline {1.10.3}References}{19}{subsection.39}

    26 \contentsline {subsection}{\numberline {1.8.6}Typesetting mathematics}{11}{subsection.37}

    26 \contentsline {subsubsection}{A Note on bibtex}{20}{section*.41}

    27 \contentsline {section}{\numberline {1.9}Sectioning and Subsectioning}{12}{section.39}

    27 \contentsline {subsection}{\numberline {1.10.4}Tables}{20}{subsection.42}

    28 \contentsline {section}{\numberline {1.10}In Closing}{12}{section.40}

    28 \contentsline {subsection}{\numberline {1.10.5}Figures}{20}{subsection.44}

    29 \contentsline {chapter}{\numberline {2}Chapter Title Here}{13}{chapter.41}

    29 \contentsline {subsection}{\numberline {1.10.6}Typesetting mathematics}{22}{subsection.46}

    30 \contentsline {section}{\numberline {2.1}Properties of $\delimiter "026E30F c$}{13}{section.42}

    30 \contentsline {section}{\numberline {1.11}Sectioning and Subsectioning}{22}{section.48}

    31 \contentsline {subsection}{\numberline {2.1.1}function $\delimiter "026E30F c$ is not 1-to-1}{13}{subsection.43}

    31 \contentsline {section}{\numberline {1.12}In Closing}{22}{section.49}

    32 \contentsline {subsection}{\numberline {2.1.2}Subsection 1}{13}{subsection.44}

    32 \contentsline {chapter}{\numberline {2}Chapter Title Here}{23}{chapter.50}

    33 \contentsline {subsection}{\numberline {2.1.3}Subsection 2}{13}{subsection.45}

    33 \contentsline {section}{\numberline {2.1}Properties of $\delimiter "026E30F c$}{23}{section.51}

    34 \contentsline {section}{\numberline {2.2}Main Section 2}{14}{section.46}

    34 \contentsline {subsection}{\numberline {2.1.1}function $\delimiter "026E30F c$ is not 1-to-1}{23}{subsection.52}

    35 \contentsline {chapter}{\numberline {3}Common Identities In Simplification-Related Functions}{15}{chapter.47}

    35 \contentsline {subsection}{\numberline {2.1.2}Subsection 1}{23}{subsection.53}

    36 \contentsline {section}{\numberline {3.1}Idempotency of $\mathit {simp}$}{15}{section.48}

    36 \contentsline {subsection}{\numberline {2.1.3}Subsection 2}{23}{subsection.54}

    37 \contentsline {subsection}{\numberline {3.1.1}Syntactic Equivalence Under $\mathit {simp}$}{15}{subsection.50}

    37 \contentsline {section}{\numberline {2.2}Main Section 2}{24}{section.55}

    38 \contentsline {subsection}{\numberline {3.1.2}Subsection 2}{15}{subsection.51}

    38 \contentsline {chapter}{\numberline {3}Common Identities In Simplification-Related Functions}{25}{chapter.56}

    39 \contentsline {section}{\numberline {3.2}Main Section 2}{15}{section.52}

    39 \contentsline {section}{\numberline {3.1}Idempotency of $\mathit {simp}$}{25}{section.57}

    40 \contentsline {chapter}{\numberline {A}Frequently Asked Questions}{17}{appendix.53}

    40 \contentsline {subsection}{\numberline {3.1.1}Syntactic Equivalence Under $\mathit {simp}$}{25}{subsection.59}

    41 \contentsline {section}{\numberline {A.1}How do I change the colors of links?}{17}{section.54}

    41 \contentsline {subsection}{\numberline {3.1.2}Subsection 2}{25}{subsection.60}

    42 \contentsline {chapter}{Bibliography}{19}{appendix*.55}

    42 \contentsline {section}{\numberline {3.2}Main Section 2}{25}{section.61}

    43 \contentsline {chapter}{\numberline {A}Frequently Asked Questions}{27}{appendix.62}

    44 \contentsline {section}{\numberline {A.1}How do I change the colors of links?}{27}{section.63}

    45 \contentsline {chapter}{Bibliography}{29}{appendix*.64}