diff --git a/doc/exploration/explore.aux b/doc/exploration/explore.aux new file mode 100644 index 000000000..d490c35e0 --- /dev/null +++ b/doc/exploration/explore.aux @@ -0,0 +1,2 @@ +\relax +\gdef \@abspage@last{2} diff --git a/doc/exploration/explore.log b/doc/exploration/explore.log new file mode 100644 index 000000000..a4705ddc6 --- /dev/null +++ b/doc/exploration/explore.log @@ -0,0 +1,382 @@ +This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024) (preloaded format=pdflatex 2024.7.9) 27 AUG 2024 16:15 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**explore.tex +(./explore.tex +LaTeX2e <2024-06-01> patch level 2 +L3 programming layer <2024-05-27> +(c:/TexLive/2024/texmf-dist/tex/latex/base/article.cls +Document Class: article 2024/02/08 v1.4n Standard LaTeX document class +(c:/TexLive/2024/texmf-dist/tex/latex/base/size10.clo +File: size10.clo 2024/02/08 v1.4n Standard LaTeX file (size option) +) +\c@part=\count194 +\c@section=\count195 +\c@subsection=\count196 +\c@subsubsection=\count197 +\c@paragraph=\count198 +\c@subparagraph=\count199 +\c@figure=\count266 +\c@table=\count267 +\abovecaptionskip=\skip49 +\belowcaptionskip=\skip50 +\bibindent=\dimen141 +) (./preamble.sty +(c:/TexLive/2024/texmf-dist/tex/latex/tools/xspace.sty +Package: xspace 2014/10/28 v1.13 Space after command names (DPC,MH) +) +(c:/TexLive/2024/texmf-dist/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2013/01/14 v3.01 AMS font symbols + +(c:/TexLive/2024/texmf-dist/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support +\@emptytoks=\toks17 +\symAMSa=\mathgroup4 +\symAMSb=\mathgroup5 +LaTeX Font Info: Redeclaring math symbol \hbar on input line 98. +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 106. +)) +(c:/TexLive/2024/texmf-dist/tex/latex/amsmath/amsmath.sty +Package: amsmath 2024/05/23 v2.17q AMS math features +\@mathmargin=\skip51 + +For additional information on amsmath, use the `?' option. +(c:/TexLive/2024/texmf-dist/tex/latex/amsmath/amstext.sty +Package: amstext 2021/08/26 v2.01 AMS text + +(c:/TexLive/2024/texmf-dist/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 generic functions +\@emptytoks=\toks18 +\ex@=\dimen142 +)) +(c:/TexLive/2024/texmf-dist/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d Bold Symbols +\pmbraise@=\dimen143 +) +(c:/TexLive/2024/texmf-dist/tex/latex/amsmath/amsopn.sty +Package: amsopn 2022/04/08 v2.04 operator names +) +\inf@bad=\count268 +LaTeX Info: Redefining \frac on input line 233. +\uproot@=\count269 +\leftroot@=\count270 +LaTeX Info: Redefining \overline on input line 398. +LaTeX Info: Redefining \colon on input line 409. +\classnum@=\count271 +\DOTSCASE@=\count272 +LaTeX Info: Redefining \ldots on input line 495. +LaTeX Info: Redefining \dots on input line 498. +LaTeX Info: Redefining \cdots on input line 619. +\Mathstrutbox@=\box52 +\strutbox@=\box53 +LaTeX Info: Redefining \big on input line 721. +LaTeX Info: Redefining \Big on input line 722. +LaTeX Info: Redefining \bigg on input line 723. +LaTeX Info: Redefining \Bigg on input line 724. +\big@size=\dimen144 +LaTeX Font Info: Redeclaring font encoding OML on input line 742. +LaTeX Font Info: Redeclaring font encoding OMS on input line 743. +\macc@depth=\count273 +LaTeX Info: Redefining \bmod on input line 904. +LaTeX Info: Redefining \pmod on input line 909. +LaTeX Info: Redefining \smash on input line 939. +LaTeX Info: Redefining \relbar on input line 969. +LaTeX Info: Redefining \Relbar on input line 970. +\c@MaxMatrixCols=\count274 +\dotsspace@=\muskip17 +\c@parentequation=\count275 +\dspbrk@lvl=\count276 +\tag@help=\toks19 +\row@=\count277 +\column@=\count278 +\maxfields@=\count279 +\andhelp@=\toks20 +\eqnshift@=\dimen145 +\alignsep@=\dimen146 +\tagshift@=\dimen147 +\tagwidth@=\dimen148 +\totwidth@=\dimen149 +\lineht@=\dimen150 +\@envbody=\toks21 +\multlinegap=\skip52 +\multlinetaggap=\skip53 +\mathdisplay@stack=\toks22 +LaTeX Info: Redefining \[ on input line 2953. +LaTeX Info: Redefining \] on input line 2954. +) +(c:/TexLive/2024/texmf-dist/tex/latex/mnsymbol/MnSymbol.sty +Package: MnSymbol 2007/01/21 v1.4 support for the MnSymbol font + +(c:/TexLive/2024/texmf-dist/tex/latex/base/textcomp.sty +Package: textcomp 2024/04/24 v2.1b Standard LaTeX package +) +LaTeX Info: Redefining \dagger on input line 84. +LaTeX Info: Redefining \ddagger on input line 84. +LaTeX Info: Redefining \mathparagraph on input line 84. +LaTeX Info: Redefining \mathsection on input line 84. +LaTeX Info: Redefining \mathdollar on input line 84. +LaTeX Info: Redefining \mathsterling on input line 84. +LaTeX Info: Redefining \yen on input line 84. +LaTeX Info: Redefining \circledR on input line 84. +LaTeX Info: Redefining \circledS on input line 84. +LaTeX Info: Redefining \Re on input line 84. +LaTeX Info: Redefining \Im on input line 84. +LaTeX Info: Redefining \dotplus on input line 84. +LaTeX Info: Redefining \thicksim on input line 84. +LaTeX Info: Redefining \thickapprox on input line 84. +LaTeX Info: Redefining \veebar on input line 84. +LaTeX Info: Redefining \barwedge on input line 84. +LaTeX Info: Redefining \doublebarwedge on input line 84. +LaTeX Info: Redefining \centerdot on input line 84. +LaTeX Info: Redefining \divideontimes on input line 84. +\symMnSyA=\mathgroup6 +\symMnSyB=\mathgroup7 +\symMnSyC=\mathgroup8 +\symMnSyD=\mathgroup9 +LaTeX Font Info: Redeclaring symbol font `largesymbols' on input line 119. +LaTeX Font Info: Overwriting symbol font `largesymbols' in version `normal' +(Font) OMX/cmex/m/n --> OMX/MnSymbolE/m/n on input line 119. +LaTeX Font Info: Overwriting symbol font `largesymbols' in version `bold' +(Font) OMX/cmex/m/n --> OMX/MnSymbolE/m/n on input line 119. +LaTeX Font Info: Redeclaring symbol font `symbols' on input line 120. +LaTeX Font Info: Encoding `OMS' has changed to `U' for symbol font +(Font) `symbols' in the math version `normal' on input line 120. +LaTeX Font Info: Overwriting symbol font `symbols' in version `normal' +(Font) OMS/cmsy/m/n --> U/MnSymbolF/m/n on input line 120. +LaTeX Font Info: Encoding `OMS' has changed to `U' for symbol font +(Font) `symbols' in the math version `bold' on input line 120. +LaTeX Font Info: Overwriting symbol font `symbols' in version `bold' +(Font) OMS/cmsy/b/n --> U/MnSymbolF/m/n on input line 120. +LaTeX Font Info: Overwriting symbol font `MnSyA' in version `bold' +(Font) U/MnSymbolA/m/n --> U/MnSymbolA/b/n on input line 121. +LaTeX Font Info: Overwriting symbol font `MnSyB' in version `bold' +(Font) U/MnSymbolB/m/n --> U/MnSymbolB/b/n on input line 122. +LaTeX Font Info: Overwriting symbol font `MnSyC' in version `bold' +(Font) U/MnSymbolC/m/n --> U/MnSymbolC/b/n on input line 123. +LaTeX Font Info: Overwriting symbol font `MnSyD' in version `bold' +(Font) U/MnSymbolD/m/n --> U/MnSymbolD/b/n on input line 124. +LaTeX Font Info: Overwriting symbol font `largesymbols' in version `bold' +(Font) OMX/MnSymbolE/m/n --> OMX/MnSymbolE/b/n on input line 1 +25. +LaTeX Font Info: Overwriting symbol font `symbols' in version `bold' +(Font) U/MnSymbolF/m/n --> U/MnSymbolF/b/n on input line 126. +LaTeX Font Info: Redeclaring math alphabet \mathcal on input line 241. +LaTeX Font Info: Overwriting math alphabet `\mathcal' in version `bold' +(Font) OMS/MnSymbolS/m/n --> OMS/MnSymbolS/b/n on input line 2 +41. +LaTeX Info: Redefining \longrightarrow on input line 548. +LaTeX Info: Redefining \longleftarrow on input line 549. +LaTeX Info: Redefining \longleftrightarrow on input line 550. +LaTeX Info: Redefining \Longrightarrow on input line 551. +LaTeX Info: Redefining \Longleftarrow on input line 552. +LaTeX Info: Redefining \Longleftrightarrow on input line 553. +LaTeX Info: Redefining \longmapsto on input line 554. +LaTeX Info: Redefining \vdots on input line 868. +LaTeX Font Info: Redeclaring math symbol \braceld on input line 1721. +LaTeX Font Info: Redeclaring math symbol \bracelu on input line 1722. +LaTeX Font Info: Redeclaring math symbol \bracerd on input line 1723. +LaTeX Font Info: Redeclaring math symbol \braceru on input line 1724. +LaTeX Info: Redefining \downbracefill on input line 1799. +LaTeX Info: Redefining \upbracefill on input line 1800. +LaTeX Info: Redefining \overbrace on input line 1819. +LaTeX Info: Redefining \underbrace on input line 1820. +LaTeX Info: Redefining \surd on input line 1843. +LaTeX Font Info: Redeclaring math accent \widehat on input line 1845. +LaTeX Font Info: Redeclaring math accent \widetilde on input line 1846. +LaTeX Font Info: Redeclaring math accent \vec on input line 1848. +) +(c:/TexLive/2024/texmf-dist/tex/latex/enumitem/enumitem.sty +Package: enumitem 2019/06/20 v3.9 Customized lists +\enitkv@toks@=\toks23 +\labelindent=\skip54 +\enit@outerparindent=\dimen151 +\enit@toks=\toks24 +\enit@inbox=\box54 +\enit@count@id=\count280 +\enitdp@description=\count281 +)) +(c:/TexLive/2024/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def +File: l3backend-pdftex.def 2024-05-08 L3 backend support: PDF output (pdfTeX) +\l__color_backend_stack_int=\count282 +\l__pdf_internal_box=\box55 +) +(./explore.aux) +\openout1 = `explore.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3. +LaTeX Font Info: ... okay on input line 3. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 3. +LaTeX Font Info: ... okay on input line 3. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 3. +LaTeX Font Info: ... okay on input line 3. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 3. +LaTeX Font Info: ... okay on input line 3. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 3. +LaTeX Font Info: ... okay on input line 3. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 3. +LaTeX Font Info: ... okay on input line 3. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 3. +LaTeX Font Info: ... okay on input line 3. +LaTeX Font Info: Trying to load font information for U+msa on input line 7. + (c:/TexLive/2024/texmf-dist/tex/latex/amsfonts/umsa.fd +File: umsa.fd 2013/01/14 v3.01 AMS symbols A +) +LaTeX Font Info: Trying to load font information for U+msb on input line 7. + +(c:/TexLive/2024/texmf-dist/tex/latex/amsfonts/umsb.fd +File: umsb.fd 2013/01/14 v3.01 AMS symbols B +) +! Undefined control sequence. +\step #1->\mapstochar + \xrightarrow {#1} +l.29 \item ${\step{} + }\subseteq P\times A\times P$ a step relation; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +\ncomesfrom ->\arrownot + \leftarrowtail +l.35 ...me} (denoted $\Prime(p)$) if $p\ncomesfrom + $, \emph{closed} (denoted ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +\ngoesto ->\arrownot + \rightarrowtail +l.35 ...osed} (denoted $\Closed(p)$) if $p\ngoesto + $ and \emph{open} (denoted... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +\step #1->\mapstochar + \xrightarrow {#1} +l.39 ... Stepping is deterministic; i.e., $\step{} + $ is a partial function fr... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +\step #1->\mapstochar + \xrightarrow {#1} +l.42 ...en to prime pseudo-states; i.e., $p\step{} + q$ implies $\Open(p)$ and ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +\step #1->\mapstochar + \xrightarrow {#1} +l.44 ...annot decrease transience; i.e., $p\step{} + q$ implies $\Tdepth(q)\geq... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + + +[1 + +{c:/TexLive/2024/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{c:/TexLive/2024/ +texmf-dist/fonts/enc/dvips/mnsymbol/MnSymbolE.enc}{c:/TexLive/2024/texmf-dist/f +onts/enc/dvips/mnsymbol/MnSymbolA.enc}{c:/TexLive/2024/texmf-dist/fonts/enc/dvi +ps/cm-super/cm-super-ts1.enc}{c:/TexLive/2024/texmf-dist/fonts/enc/dvips/mnsymb +ol/MnSymbolD.enc}{c:/TexLive/2024/texmf-dist/fonts/enc/dvips/mnsymbol/MnSymbolC +.enc}] +! Undefined control sequence. +\step #1->\mapstochar + \xrightarrow {#1} +l.60 ...\cls p\trans a \cls{p'}$ for all $p\step a + p'$; i.e., $s\trans a s'$... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +\step #1->\mapstochar + \xrightarrow {#1} +l.60 ...., $s\trans a s'$ if $s\comesfrom^*\step a + \goesto^* s'$; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +\pto ->\lhook + \joinrel \to +l.65 ...ation} is a partial function $C:\cls P\pto + P$. $C$ gives rise to a s... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +\step #1->\mapstochar + \xrightarrow {#1} +l.69 ...$s\trans a s'$ if $C(s)\comesfrom^*\step a + \goesto^* C(s')$; +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + + +[2] (./explore.aux) + *********** +LaTeX2e <2024-06-01> patch level 2 +L3 programming layer <2024-05-27> + *********** + ) +Here is how much of TeX's memory you used: + 4429 strings out of 473584 + 60866 string characters out of 5732364 + 1937908 words of memory out of 5000000 + 27298 multiletter control sequences out of 15000+600000 + 575315 words of font info for 95 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 71i,13n,79p,241b,221s stack positions out of 10000i,1000n,20000p,200000b,200000s + +Output written on explore.pdf (2 pages, 121421 bytes). +PDF statistics: + 75 PDF objects out of 1000 (max. 8388607) + 47 compressed objects within 1 object stream + 0 named destinations out of 1000 (max. 500000) + 1 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/doc/exploration/explore.pdf b/doc/exploration/explore.pdf new file mode 100644 index 000000000..d68fa6f06 Binary files /dev/null and b/doc/exploration/explore.pdf differ diff --git a/doc/exploration/explore.synctex.gz b/doc/exploration/explore.synctex.gz new file mode 100644 index 000000000..3a7b79217 Binary files /dev/null and b/doc/exploration/explore.synctex.gz differ diff --git a/doc/exploration/explore.tex b/doc/exploration/explore.tex new file mode 100644 index 000000000..02e5deac8 --- /dev/null +++ b/doc/exploration/explore.tex @@ -0,0 +1,73 @@ +\documentclass{article} +\usepackage{preamble} +\begin{document} +\title{Fundamentals of exploration in \GROOVE} +\author{Arend Rensink} +\date{August 2024} +\maketitle + +\medskip\noindent +We globally assume a set of labels $A$. + +\medskip\noindent +A state space is a tuple $\tupof{S,{\ra},{\up},\Tdepth}$ with +\begin{itemize} +\item $S$ a set of states; +\item ${\ra}\subseteq S\times A\times S$ a transition relation; +\item ${\up}\subseteq S$ a termination predicate; +\item ${\Tdepth}:S\to \natN$ a \emph{transient depth} (or \emph{transience}) function. +\end{itemize} +% +State $s\in S$ is called \emph{final} if $p\up$, \emph{transient} (denoted $\Trnt(s)$) if $\Tdepth(s)>0$ and \emph{stable} (denoted $\Stable(s)$) if $\Tdepth(s)=0$. + +\medskip\noindent State spaces are generated from a \emph{pseudo-state spaces}. + +\medskip\noindent +A pseudo-state space is a tuple $\tupof{P,{\mapsto},{\goesto},{\up},\Tdepth}$ with +\begin{itemize} +\item $P$ a finite set of pseudo-states; +\item ${\step{}}\subseteq P\times A\times P$ a step relation; +\item ${\goesto}: P\times P$ a partial, acyclic evolution relation; +\item ${\up} \subseteq P$ a termination predicate; +\item ${\Tdepth}:S\to \natN$ a \emph{transient depth} function. +\end{itemize} +% +Pseudo-state $p\in P$ is called \emph{prime} (denoted $\Prime(p)$) if $p\ncomesfrom$, \emph{closed} (denoted $\Closed(p)$) if $p\ngoesto$ and \emph{open} (denoted $\Open(p)$) if it is not closed. +% +A pseudo-state space is \emph{well-formed} if it satisfies the following additional properties: +\begin{itemize} +\item Stepping is deterministic; i.e., $\step{}$ is a partial function from $P$ to $A\times P$; +\item Evolution is deterministic; i.e., $\goesto$ is a partial function from $P$ to $P$; +\item Evolution is injective; i.e., $\comesfrom$ is a partial function from $P$ to $P$; +\item All steps go from open to prime pseudo-states; i.e., $p\step{}q$ implies $\Open(p)$ and $\Prime(q)$; +\item All final pseudo-states are stable and closed; i.e., $p\up$ implies $\Stable(p)$ and $\Closed(p)$; +\item Stepping cannot decrease transience; i.e., $p\step{}q$ implies $\Tdepth(q)\geq \Tdepth(p)$; +\item Evolution cannot increase transience; i.e., $p\goesto q$ implies $\Tdepth(q)\leq \Tdepth(p)$. +\end{itemize} +From now on, we only deal with well-formed pseudo-states spaces. The \emph{prime of} and \emph{closure of} a pseudo-state $p$ are defined as +\begin{align*} + \prm p & = q \quad \text{where $\Prime (q)$ and $q\goesto^* p$} \\ + \cls p & = q \quad \text{where $\Closed(q)$ and $p\comesfrom^* q$} \enspace. +\end{align*} +% +Note that these are well-defined because $P$ is finite and $\goesto$ is acyclic, deterministic and injective. + +\medskip\noindent +A pseudo-state space $\tupof{P,{\mapsto},{\goesto},{\up},\Tdepth}$ gives rise to a state space $\tupof{S,\trans{},\up,\Tdepth_S}$ where +% +\begin{itemize} +\item $s\in S$ if $s$ is a closed pseudo-state; i.e., $S=\cls P$; +\item $\cls p\trans a \cls{p'}$ for all $p\step a p'$; i.e., $s\trans a s'$ if $s\comesfrom^*\step a \goesto^* s'$; +\item $\up$ remains unchanged (noting that $p\up$ implies $\Closed(p)$ and hence $p\in S$); +\item $\Tdepth_S$ restricts $\Tdepth$ to $S$; i.e., $\Tdepth_S=\gensetof{(p,\Tdepth(p))}{p\in S}$. +\end{itemize} +% +Given a pseudo-state space $P$, a \emph{configuration} is a partial function $C:\cls P\pto P$. $C$ gives rise to a state space $\tupof{S_C,\trans{}_C,\up_C,\Tdepth_C}$ where +% +\begin{itemize} +\item $S_C=\dom C$; +\item For all $s,s'\in S_C$, $s\trans a s'$ if $C(s)\comesfrom^*\step a \goesto^* C(s')$; +\item For all $s\in S_C$, $s\up_C$ if $C(s)\up$; +\item For all $s\in S_C$, $\Tdepth_C(s)=\Tdepth(C(s))$. +\end{itemize} +\end{document} diff --git a/doc/exploration/preamble.sty b/doc/exploration/preamble.sty new file mode 100644 index 000000000..e48969175 --- /dev/null +++ b/doc/exploration/preamble.sty @@ -0,0 +1,68 @@ +\usepackage{xspace} +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage{MnSymbol} +%\usepackage{stmaryrd} +\usepackage[inline]{enumitem} +\setlist{itemsep=0pt} + +\newcommand{\GROOVE}{GROOVE} + +\newcommand{\cls}[1]{{#1}\mskip1mu\triangleright} +\newcommand{\prm}[1]{\triangleleft\mskip1mu{#1}} + +\newcommand{\dom}{\mathop{\mathrm{dom}}} + +\newcommand{\Prime}{\ensuremath{\mathit{prime}}} +\newcommand{\Done}{\ensuremath{\mathit{done}}} +\newcommand{\Open}{\ensuremath{\mathit{open}}} +\newcommand{\Closed}{\ensuremath{\mathit{closed}}} +\newcommand{\Trnt}{\ensuremath{\mathit{trnt}}} +\newcommand{\Abs}{\ensuremath{\mathit{abs}}} +\newcommand{\Stable}{\ensuremath{\mathit{stable}}} +\newcommand{\Tdepth}{\ensuremath{\mathit{tdp}}} + +\newcommand{\cC}{\mathcal{C}} +\newcommand{\natN}{\mathbb{N}} + +\newcommand{\setof}[1]{\{{#1}\}} +\newcommand{\gensetof}[2]{\setof{{#1}\mid{#2}}} +\newcommand{\tupof}[1]{\langle{#1}\rangle} +\newcommand{\iffdef}{:\Leftrightarrow} + +% Special arrows +\newcommand{\pto}{\lhook\joinrel\to} +\newcommand{\goesto}{\rightarrowtail} +\newcommand{\ngoesto}{\arrownot\rightarrowtail} +\newcommand{\comesfrom}{\leftarrowtail} +\newcommand{\ncomesfrom}{\arrownot\leftarrowtail} +\newcommand{\ra}{\rightarrow} +\newcommand{\up}{{\uparrow}} +\newcommand{\Up}{{\Uparrow}} + + +%%%% definition of extensible "transition arrows" +% +% auxiliaries +\newcommand{\linefill}{% + \cleaders + \hbox{$\smash{\mkern-2mu\mathord-\mkern-2mu}$}% + \hfill + \vphantom{\lower1pt\hbox{$\rightarrow$}}% +} +\newcommand{\Linefill}{% + \cleaders + \hbox{$\smash{\mkern-2mu\mathord=\mkern-2mu}$}% + \hfill + \vphantom{\hbox{$\Rightarrow$}}% +} + +% single-arrow transition +\newcommand{\trans}[1]{\xrightarrow{#1}}% +% negative single-arrow transition +\newcommand{\ntrans}[1]{\not\xrightarrow{#1}} + +% mapsto-like transition +\newcommand{\step}[1]{\mapstochar\xrightarrow{#1}} +% negative mapsto-like transition +\newcommand{\nstep}[1]{\not\mapstochar\joinrel\xrightarrow{#1}} diff --git a/doc/exploration/texput.log b/doc/exploration/texput.log new file mode 100644 index 000000000..48c78403a --- /dev/null +++ b/doc/exploration/texput.log @@ -0,0 +1,21 @@ +This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024) (preloaded format=pdflatex 2024.7.9) 27 AUG 2024 16:15 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**preamble.tex + +! Emergency stop. +<*> preamble.tex + +*** (job aborted, file error in nonstop mode) + + +Here is how much of TeX's memory you used: + 3 strings out of 473584 + 104 string characters out of 5732364 + 1925908 words of memory out of 5000000 + 22997 multiletter control sequences out of 15000+600000 + 558069 words of font info for 36 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 0i,0n,0p,1b,6s stack positions out of 10000i,1000n,20000p,200000b,200000s +! ==> Fatal error occurred, no output PDF file produced!