mirror of
https://github.com/kuhyx/WUT_Computer_Science.git
synced 2026-07-04 14:43:08 +02:00
Finishing third task
This commit is contained in:
parent
336034e260
commit
56a288d5a0
@ -21,7 +21,10 @@
|
||||
\@writefile{lof}{\contentsline {figure}{\numberline {1.9}{\ignorespaces Operator '$a^*+ba^*b + bba^*$'}}{3}{}\protected@file@percent }
|
||||
\newlabel{fig:final}{{1.9}{3}}
|
||||
\@writefile{lof}{\contentsline {figure}{\numberline {1.10}{\ignorespaces Operator '$a^*+ba^*b + bba^*$' - changed names of states}}{3}{}\protected@file@percent }
|
||||
\newlabel{fig:final}{{1.10}{3}}
|
||||
\newlabel{fig:finalBetter}{{1.10}{3}}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1.4}Transforming NFA into DFA using subset algorithm}{4}{}\protected@file@percent }
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1.5}Constructing minimal state DFA}{4}{}\protected@file@percent }
|
||||
\gdef \@abspage@last{5}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.1}State table}{4}{}\protected@file@percent }
|
||||
\@writefile{lof}{\contentsline {figure}{\numberline {1.11}{\ignorespaces DFA graph before minimalization}}{5}{}\protected@file@percent }
|
||||
\newlabel{dfaNominimalization}{{1.11}{5}}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1.5}Constructing minimal state DFA}{5}{}\protected@file@percent }
|
||||
\gdef \@abspage@last{6}
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
# Fdb version 3
|
||||
["pdflatex"] 1637106796 "project.tex" "project.pdf" "project" 1637118524
|
||||
["pdflatex"] 1637121514 "project.tex" "project.pdf" "project" 1637121515
|
||||
"/etc/texmf/web2c/texmf.cnf" 1635008344 475 c0e671620eb5563b2130f56340a5fde8 ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df ""
|
||||
@ -18,10 +18,12 @@
|
||||
"/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm" 1136768653 1120 8b7d695260f3cff42e636090a8002094 ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb" 1248133631 32080 340ef9bf63678554ee606688e7b5339d ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1248133631 36299 5f9df58c2139e7edcf37c8fca4bd384d ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb" 1248133631 36281 c355509802a035cadc5f15869451dcee ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1248133631 35752 024fb6c41858982481f6968b5fc26508 ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb" 1248133631 32722 d7379af29a190c3f453aba36302ff5a9 ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb" 1248133631 32362 179c33bbf43f19adbb3825bb4e36e57a ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1248133631 32762 224316ccc9ad3ca0423a14971cfa7fc1 ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1248133631 32569 5e5ddc8df908dea60932f3c484a54c0d ""
|
||||
"/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb" 1248133631 32716 08e384dc442464e7285e891af9f45947 ""
|
||||
"/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1461363279 71627 94eb9990bed73c364d7f53f960cc8c5b ""
|
||||
"/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty" 1583617216 6501 4011d89d9621e0b0901138815ba5ff29 ""
|
||||
@ -123,9 +125,9 @@
|
||||
"/usr/share/texmf/web2c/texmf.cnf" 1613593815 38841 799d1dd9682a55ce442e10c99777ecc1 ""
|
||||
"/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1635008389 5160710 ecf427ae8fa19139d8691f526e47bb9b ""
|
||||
"/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1635008460 2570450 6e12b1c097cbda0f70015645294afd24 ""
|
||||
"project.aux" 1637106797 2301 25365c128ec31bbdc3fbc64fe64f1084 "pdflatex"
|
||||
"project.tex" 1637118524 13317 96fad0bd37e24e817d231aeb954632f1 ""
|
||||
"project.aux" 1637121515 2592 65a2c5d3cc5d4fbb767d5e48f951d8a4 "pdflatex"
|
||||
"project.tex" 1637121514 16514 c0b41610a76b6798be6eeebc2a81d40a ""
|
||||
(generated)
|
||||
"project.aux"
|
||||
"project.pdf"
|
||||
"project.aux"
|
||||
"project.log"
|
||||
|
||||
@ -517,11 +517,14 @@ INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr12.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm
|
||||
INPUT project.aux
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb
|
||||
|
||||
42
project.log
42
project.log
@ -1,4 +1,4 @@
|
||||
This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/Debian) (preloaded format=pdflatex 2021.10.23) 17 NOV 2021 00:53
|
||||
This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020/Debian) (preloaded format=pdflatex 2021.10.23) 17 NOV 2021 04:58
|
||||
entering extended mode
|
||||
restricted \write18 enabled.
|
||||
file:line:error style messages enabled.
|
||||
@ -335,11 +335,7 @@ File: tikzlibrarypositioning.code.tex 2020/12/27 v3.1.8b (3.1.8b)
|
||||
File: l3backend-pdftex.def 2020-01-29 L3 backend support: PDF output (pdfTeX)
|
||||
\l__color_backend_stack_int=\count285
|
||||
\l__pdf_internal_box=\box80
|
||||
) (./project.aux
|
||||
|
||||
LaTeX Warning: Label `fig:final' multiply defined.
|
||||
|
||||
)
|
||||
) (./project.aux)
|
||||
\openout1 = `project.aux'.
|
||||
|
||||
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 16.
|
||||
@ -415,26 +411,32 @@ Overfull \hbox (34.79312pt too wide) in paragraph at lines 446--447
|
||||
[][]
|
||||
[]
|
||||
|
||||
[1] [2] [3] [4
|
||||
[1] [2] [3]
|
||||
Overfull \hbox (61.62515pt too wide) detected at line 454
|
||||
\OML/cmm/m/it/10 ^^O[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 move\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ; a\OT1/cmr/m/n/10 )) = (\OML/cmm/m/it/10 ^^O[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 move\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 q[]; q[]; q[]; q[]; q[]; q[]; q[]; []; a\OT1/cmr/m/n/10 ))) = \OML/cmm/m/it/10 ^^O[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 q[]\OT1/cmr/m/n/10 ) = (\OML/cmm/m/it/10 q[]; q[]; q[]; []\OT1/cmr/m/n/10 ) = []
|
||||
[]
|
||||
|
||||
] (./project.aux)
|
||||
|
||||
LaTeX Warning: There were multiply-defined labels.
|
||||
Overfull \hbox (58.9759pt too wide) detected at line 455
|
||||
\OML/cmm/m/it/10 A \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 ^^O[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 move\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ; b\OT1/cmr/m/n/10 )) = \OML/cmm/m/it/10 ^^O[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 move\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 q[]; q[]; q[]; q[]; q[]; q[]; q[]; []; b\OT1/cmr/m/n/10 ))) = \OML/cmm/m/it/10 ^^O[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 q[]; q[]\OT1/cmr/m/n/10 ) = (\OML/cmm/m/it/10 q[]; q[]\OT1/cmr/m/n/10 ) = \OML/cmm/m/it/10 C
|
||||
[]
|
||||
|
||||
)
|
||||
[4
|
||||
|
||||
] [5] (./project.aux) )
|
||||
Here is how much of TeX's memory you used:
|
||||
13885 strings out of 479304
|
||||
290077 string characters out of 5869778
|
||||
665548 words of memory out of 5000000
|
||||
30830 multiletter control sequences out of 15000+600000
|
||||
408198 words of font info for 44 fonts, out of 8000000 for 9000
|
||||
13908 strings out of 479304
|
||||
290559 string characters out of 5869778
|
||||
665530 words of memory out of 5000000
|
||||
30853 multiletter control sequences out of 15000+600000
|
||||
408505 words of font info for 45 fonts, out of 8000000 for 9000
|
||||
1141 hyphenation exceptions out of 8191
|
||||
113i,10n,116p,418b,915s stack positions out of 5000i,500n,10000p,200000b,80000s
|
||||
</usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb>
|
||||
Output written on project.pdf (5 pages, 90541 bytes).
|
||||
113i,10n,116p,418b,949s stack positions out of 5000i,500n,10000p,200000b,80000s
|
||||
</usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb>
|
||||
Output written on project.pdf (6 pages, 114865 bytes).
|
||||
PDF statistics:
|
||||
51 PDF objects out of 1000 (max. 8388607)
|
||||
36 compressed objects within 1 object stream
|
||||
62 PDF objects out of 1000 (max. 8388607)
|
||||
44 compressed objects within 1 object stream
|
||||
0 named destinations out of 1000 (max. 500000)
|
||||
13 words of extra memory for PDF output out of 10000 (max. 10000000)
|
||||
|
||||
|
||||
BIN
project.pdf
BIN
project.pdf
Binary file not shown.
Binary file not shown.
85
project.tex
85
project.tex
@ -1,4 +1,4 @@
|
||||
\documentclass{report}
|
||||
\documentclass{report}[pt12]
|
||||
\usepackage{amsmath}
|
||||
\usepackage{tikz}
|
||||
\usepackage[section]{placeins}
|
||||
@ -444,10 +444,91 @@ We are given following regular expression:
|
||||
% bba*
|
||||
|
||||
\end{tikzpicture}
|
||||
\caption{Operator '$a^*+ba^*b + bba^*$' - changed names of states} \label{fig:final}
|
||||
\caption{Operator '$a^*+ba^*b + bba^*$' - changed names of states} \label{fig:finalBetter}
|
||||
\end{figure}
|
||||
|
||||
\section{Transforming NFA into DFA using subset algorithm}
|
||||
I will use $\epsilon_{cl}$ instead of $\epsilon$-closure for brevity sake.
|
||||
Final state - $\underline{q_{19}}$ was marked with an $\underline{underline}$ and so did all the states of DFA that contain it.
|
||||
\[ A = \epsilon_{cl}(q_0) = (q_0, q_1, q_3, q_4, q_6, q_{12}, q_{18}, \underline{q_{19}}) = \underline{A} \]
|
||||
\[ \epsilon_{cl}(move(\underline{A}, a)) = (\epsilon_{cl}(move(q_0, q_1, q_3, q_4, q_6, q_{12}, q_{18}, \underline{q_{19}}, a))) = \epsilon_{cl}(q_9) = (q_9, q_{12}, q_{18}, \underline{q_{19}}) = \underline{B} \]
|
||||
\[ A = \epsilon_{cl}(move(\underline{A}, b)) = \epsilon_{cl}(move(q_0, q_1, q_3, q_4, q_6, q_{12}, q_{18}, \underline{q_{19}}, b))) = \epsilon_{cl}(q_2, q_7) = (q_{10}, q_{15}) = C \]
|
||||
\[ \epsilon_{cl}(move(\underline{B}, a)) = \epsilon_{cl}(move(q_9, q_{12}, q_{18}, \underline{q_{19}}), a) = \emptyset \]
|
||||
\[ \epsilon_{cl}(move(\underline{B}, b)) = \epsilon_{cl}(move(q_9, q_{12}, q_{18}, \underline{q_{19}}), b) = \emptyset \]
|
||||
\[ \epsilon_{cl}(move(C, a)) = \epsilon_{cl}(move(q_{10}, q_{15}), a) = \epsilon_{cl}(q_{13}) = (q_{15}) = D \]
|
||||
\[ \epsilon_{cl}(move(C, b)) = \epsilon_{cl}(move(q_{10}, q_{15}), b) = \epsilon_{cl}(q_{17}) = (q_{18}, \underline{q_{19}}) = \underline{E} \]
|
||||
\[ \epsilon_{cl}(move(D, a)) = \epsilon_{cl}(move((q_{15}), a) = \epsilon_{cl}(\emptyset) = \emptyset \]
|
||||
\[ \epsilon_{cl}(move(D, b)) = \epsilon_{cl}(move((q_{15}), b) = \epsilon_{cl}(q_{17}) = (q_{18}, \underline{q_{19}}) = \underline{E} \]
|
||||
\[ \epsilon_{cl}(move(\underline{E}, a)) = \epsilon_{cl}(move((q_{18}, \underline{q_{19}}), a) = \epsilon_{cl}(\emptyset) = \emptyset \]
|
||||
\[ \epsilon_{cl}(move(\underline{E}, b)) = \epsilon_{cl}(move((q_{18}, \underline{q_{19}}), b) = \epsilon_{cl}(\emptyset) = \emptyset \]
|
||||
|
||||
\subsection{State table}
|
||||
\begin{center}
|
||||
\begin{tabular}{||c c c||}
|
||||
\hline
|
||||
State & a & b \\
|
||||
\hline
|
||||
$\underline{A}$ & $\underline{B}$ & C\\
|
||||
\hline
|
||||
$\underline{B}$ & $\emptyset$ & $\emptyset$ \\
|
||||
\hline
|
||||
C & D & $\underline{E}$\\
|
||||
\hline
|
||||
D & $\emptyset$ & $\underline{E}$\\
|
||||
\hline
|
||||
$\underline{E}$ & $\emptyset$ & $\emptyset$\\
|
||||
\hline
|
||||
$\emptyset$ & $\emptyset$ & $\emptyset$\\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{tikzpicture} [node distance = 2cm, on grid, auto]
|
||||
|
||||
\node (q0) [state, accepting, initial, initial text = {}] {A};
|
||||
\node (q1) [state, accepting, above right = of q0] {B};
|
||||
\node (q2) [state, below right = of q0] {C};
|
||||
\node (q3) [state, accepting, above right = of q2] {E};
|
||||
\node (q4) [state, below right = of q2] {D};
|
||||
\node (q5) [state, right = of q1] {$\emptyset$};
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q0) edge node {$a$} (q1);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q0) edge node {$b$} (q2);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q2) edge node {$a$} (q4);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q2) edge node {$b$} (q3);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q4) edge node {$b$} (q3);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q1) edge [bend left] node {$a, b$} (q5);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q3) edge node {$a, b$} (q5);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q4) edge [bend right] node {$a$} (q5);
|
||||
|
||||
\path [-stealth, thick]
|
||||
(q5) edge [loop] node {$a, b$} (q5);
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\end{tikzpicture}
|
||||
\caption{DFA graph before minimalization} \label{dfaNominimalization}
|
||||
\end{figure}
|
||||
|
||||
\section{Constructing minimal state DFA}
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user