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Krzysztof kuhy Rudnicki
ffa5dad02a
The 250-line cap applies to prose too, and the reports were the worst
offenders -- ENUME's projectA.tex alone was 1,876 lines. Each is now a
preamble plus one \input{} per section, which is how a long LaTeX document is
normally organised; not one byte of prose was rewritten.
"The PDF is unchanged" is checked by a script rather than by eye, because
hashing the PDF cannot work: pdflatex stamps a /CreationDate and an /ID into
every build, so two runs of the SAME source already differ. tex_fingerprint.sh
compares what a reader sees instead -- page count plus a hash of the extracted
text -- and it is stable across rebuilds of untouched sources, which is the
property that makes it usable as a gate.
It earned its keep immediately. Both ECOTE reports quote an example LaTeX
document inside an lstlisting block, so \end{document} appears in the middle
of the file; splitting on the FIRST one stranded everything after it. Same
page count, different text, caught automatically. EOPSY lab3 exposed a second
bug: a \section{} title that runs onto the next line.
Result: 19 .tex over the cap -> 1. The survivor,
ELAC/.../03-building-nfa-...tex, is 418 lines of consecutive tikz figures
with no subsection to split on and needs a hand-placed boundary.
Verified: 29 splits across two passes (section, then subsection for the
pieces still over), every one reporting `unchanged` from
scripts/tex_fingerprint.sh --check.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_0172dj34FDpao6wsix8ZuCzE
85 lines
3.5 KiB
TeX
85 lines
3.5 KiB
TeX
\section{Transforming NFA into DFA using subset algorithm}
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I will use $\epsilon_{cl}$ instead of $\epsilon$-closure for brevity sake.
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Final state - $\underline{q_{19}}$ was marked with an $\underline{underline}$ and so did all the states of DFA that contain it.
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\[ A = \epsilon_{cl}(q_0) = (q_0, q_1, q_3, q_4, q_6, q_{12}, q_{18}, \underline{q_{19}}) = \underline{A} \]
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\[ \epsilon_{cl}(move(\underline{A}, a)) = (\epsilon_{cl}(move(q_0, q_1, q_3, q_4, q_6, q_{12}, q_{18}, \underline{q_{19}}, a))) = \epsilon_{cl}(q_9) = (q_6, q_9, q_{12}, q_{18}, \underline{q_{19}}) = \underline{B} \]
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\[ A = \epsilon_{cl}(move(\underline{A}, b)) = \epsilon_{cl}(move(q_0, q_1, q_3, q_4, q_6, q_{12}, q_{18}, \underline{q_{19}}, b))) = \epsilon_{cl}(q_2, q_7) = (q_2, q_7, q_{10}, q_{15}) = C \]
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\[ \epsilon_{cl}(move(\underline{B}, a)) = \epsilon_{cl}(move(q_6, q_9, q_{12}, q_{18}, \underline{q_{19}}), a) = \epsilon_{cl}(q_9) = (q_6, q_9, q_{12}, q_{18}, \underline{q_{19}}) = \underline{B} \]
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\[ \epsilon_{cl}(move(\underline{B}, b)) = \epsilon_{cl}(move(q_6, q_9, q_{12}, q_{18}, \underline{q_{19}}), b) = \emptyset \]
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\[ \epsilon_{cl}(move(C, a)) = \epsilon_{cl}(move(q_2, q_7, q_{10}, q_{15}), a) = \epsilon_{cl}(q_{13}) = (q_{10}, q_{13}, q_{15}) = D \]
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\[ \epsilon_{cl}(move(C, b)) = \epsilon_{cl}(move((q_2, q_7, q_{10}, q_{15}), b) = \epsilon_{cl}(q_{17}) = (q_{17}, q_{18}, \underline{q_{19}}) = \underline{E} \]
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\[ \epsilon_{cl}(move(D, a)) = \epsilon_{cl}(move((q_{10}, q_{13}, q_{15}), a) = \epsilon_{cl}(q_{13}) = (q_{10}, q_{13}, q_{15}) = D \]
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\[ \epsilon_{cl}(move(D, b)) = \epsilon_{cl}(move(q_{10}, q_{13}, q_{15}, b) = \epsilon_{cl}(q_{17}) = (q_{17}, q_{18}, \underline{q_{19}}) = \underline{E} \]
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\[ \epsilon_{cl}(move(\underline{E}, a)) = \epsilon_{cl}(move(q_{17}, q_{18}, \underline{q_{19}}), a) = \epsilon_{cl}(\emptyset) = \emptyset \]
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\[ \epsilon_{cl}(move(\underline{E}, b)) = \epsilon_{cl}(move(q_{17}, q_{18}, \underline{q_{19}}), b) = \epsilon_{cl}(\emptyset) = \emptyset \]
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\subsection{State table}
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\begin{center}
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\begin{tabular}{||c c c||}
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\hline
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State & a & b \\
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\hline
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$\underline{A}$ & $\underline{B}$ & C\\
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\hline
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$\underline{B}$ & $\underline{B}$ & $\emptyset$ \\
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\hline
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C & D & $\underline{E}$\\
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\hline
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D & D & $\underline{E}$\\
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\hline
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$\underline{E}$ & $\emptyset$ & $\emptyset$\\
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\hline
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$\emptyset$ & $\emptyset$ & $\emptyset$\\
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\hline
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\end{tabular}
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\end{center}
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\begin{figure}[!htb]
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\centering
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\begin{tikzpicture} [node distance = 2cm, on grid, auto]
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\node (q0) [state, accepting, initial, initial text = {}] {A};
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\node (q1) [state, accepting, above right = of q0] {B};
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\node (q2) [state, below right = of q0] {C};
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\node (q3) [state, accepting, above right = of q2] {E};
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\node (q4) [state, below right = of q2] {D};
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\node (q5) [state, right = of q1] {$\emptyset$};
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\path [-stealth, thick]
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(q0) edge node {$a$} (q1);
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\path [-stealth, thick]
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(q0) edge node {$b$} (q2);
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\path [-stealth, thick]
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(q1) edge [loop] node {$a$} (q1);
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\path [-stealth, thick]
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(q2) edge node {$b$} (q4);
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\path [-stealth, thick]
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(q2) edge node {$b$} (q3);
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\path [-stealth, thick]
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(q4) edge [bend right] node {$b$} (q3);
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\path [-stealth, thick]
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(q4) edge [loop] node {$a$} (q4);
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\path [-stealth, thick]
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(q1) edge [bend left] node {$a$} (q5);
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\path [-stealth, thick]
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(q3) edge node {$a, b$} (q5);
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\path [-stealth, thick]
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(q5) edge [loop] node {$a, b$} (q5);
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\end{tikzpicture}
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\caption{DFA graph before minimalization} \label{dfaNominimalization}
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\end{figure}
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