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diff --git a/Master/texmf-dist/doc/latex/membranecomputing/membranecomputing.tex b/Master/texmf-dist/doc/latex/membranecomputing/membranecomputing.tex new file mode 100644 index 00000000000..a8c9207207c --- /dev/null +++ b/Master/texmf-dist/doc/latex/membranecomputing/membranecomputing.tex @@ -0,0 +1,486 @@ +\documentclass{article} + +\usepackage[utf8]{inputenc} + +\usepackage{membranecomputing} +\usepackage{hyperref} +\usepackage{enumitem} +\usepackage{amssymb} +\usepackage{longtable} + +\title{Package \texttt{membranecomputing} (v0.1)} +\author{David Orellana-MartÃn \\ \texttt{\href{mailto:dorellana@us.es}{dorellana@us.es}}} +\begin{document} + +\maketitle + +\tableofcontents + +\section{Introduction} +\label{sec:introduction} + +Membrane computing is a framework where different models of +computations, called membrane systems or P systems arise from. The +notation of these models is very variate since the number of +researchers in the area is very high, and also their background is +different, and therefore the notation can slightly change. The idea of +this package is to cover all the possible variants in the area and +their respective rules. Concerning the rules, the objective is +twofold: On the one hand, to use commands to transcript a rule in a +paper format; On the other hand, since P-Lingua is the \textit{de + facto} standard language for simulating P systems, there is a +possibility to print the rules in the P-Lingua language, ready to be +copied and pasted into a \texttt{.pli} file. + +\section{Package options} +\label{sec:package-options} + +The \texttt{membranecomputing} package offers the option +\texttt{blackboard}. The differences of this option can be found in +Subsection~\ref{sec:font-option}. + +\subsection{Font option} +\label{sec:font-option} + +Notation of P systems can change depending on the model. But even with +the same model, some differences can be found between different +papers. For instance, while some researchers use the symbol $\Gamma$ +to denote the working alphabet, other use the letter $O$. Other +example is the use of the letters $\mathcal{M}_{i}$ or $w_{i}$ for +describing the initial multisets of the regions. For this purpose, +this option has been implemented. + +\begin{itemize} +\item \texttt{traditional} (\textit{Default}) This typesets the + symbols like + $\Gamma, \Sigma, \mathcal{M}_{i}, \mathcal{R}_{i}, + \rho_{i}$~\footnote{For SNP systems, the singleton $\{a\}$, is still + called $O$ in this mode.}. +\item \texttt{blackboard} This typesets the symbols like + $O, E, w_{i}, R_{i}, p_{i}$. +\end{itemize} + +The rest of the symbols are defined without taking into account this option. + +\section{Using the package} +\label{sec:using-package} + +In this section I will try to explain all the different uses of this +package, from basic use to creation of new templates. + +\subsection{Basic notations} +\label{sec:basic-notations} + +This is a list of some notations that can be used for defining initial +multisets, sets of rules, and so on. + +\vspace{1mm} + +$ +\begin{array}{lll} + \mbox{Working alphabet} & \verb=\wa= & \wa \\ + \mbox{Input alphabet} & \verb=\ia= & \ia \\ + \mbox{Labels set} & \verb=\ls= & \ls \\ + \mbox{Membrane structure} & \verb=\ms= & \ms \\ + \mbox{Initial multiset} & \verb=\im{i}= & \im{i} \\ + \mbox{Rule set} & \verb=\rs{i}= & \rs{i} \\ + \mbox{Probabilities set} & \verb=\ps{i}= & \ps{i} \\ + \mbox{vE} & \verb=\vE= & \vE \\ + \mbox{Neuron} & \verb=\neuron{i}= & \neuron{i} \\ + \mbox{Compartment} & \verb=\compartment{i}= & \compartment{i} \\ + \mbox{Agent} & \verb=\agent{i}= & \agent{i} \\ + \mbox{Degree} & \verb=\degree= & \degree \\ + \mbox{Synapses} & \verb=\syn= & \syn \\ + \mbox{Input region} & \verb=\iin= & \iin \\ + \mbox{Output region} & \verb=\iout= & \iout \\ + \mbox{Object yes} & \verb=\yes= & \yes \\ + \mbox{Object no} & \verb=\no= & \no \\ +\end{array} +$ + +\subsection{Languages and computability theory} +\label{sec:lang-comp-theory} + +$ +\begin{array}{lll} + \mbox{Regular language} & \verb=\REG= & \REG \\ + \mbox{Linear language} & \verb=\LIN= & \LIN \\ + \mbox{Context-free language} & \verb=\CF= & \CF \\ + \mbox{Context-sensitive language} & \verb=\CS= & \CS \\ + \mbox{Recursively enumerable language} & \verb=\RE= & \RE \\ +\end{array} +$ + +To define a new set of languages, it is enough to make a new command +as follows: + +\begin{verbatim} +\newcommand{\L}{\compSet{L}} +\end{verbatim} + +This results in: $\compSet{L}$. + +\subsection{Families of membrane systems} +\label{sec:famil-membr-syst} + +Since the number of ``ingredients'' of the different variants of P +systems is sometimes high, then some notations can be used to short +them whenever they must be used. For instance, polarizationless P +systems with active membranes when dissolution rules and division +rules only for elementary membranes are allowed is usually denoted as +$\AMO{-d, +ne}$. To denote this, it is enough to write +\verb=\AM0{d, +ne}=. In this package, some examples of different +families of P systems are defined. + +$ +\begin{array}{lll} + \mbox{Ps with am} & \verb=\AM[\alpha]{\beta}= & \AM[\alpha]{\beta} \\ + \mbox{Polarizationless Ps with am} & \verb=\AMO{\alpha}= & \AMO{\alpha} \\ + \mbox{Tissue Ps with s/a rules} & \verb=\TC[\alpha]{\beta}= & \TC[\alpha]{\beta} \\ + \mbox{Tissue Ps with s/a and division rules} & \verb=\TDC{\alpha}= & \TDC{\alpha} \\ + \mbox{Tissue Ps with s/a and separation rules} & \verb=\TSC{\alpha}= & \TSC{\alpha} \\ + \mbox{Ps with s/a rules} & \verb=\CC[\alpha]{\beta}= & \CC[\alpha]{\beta} \\ + \mbox{Ps with s/a and division rules} & \verb=\CDC{\alpha}= & \CDC{\alpha} \\ + \mbox{Ps with s/a and separation rules} & \verb=\CSC{\alpha}= & \CSC{\alpha} \\ + \mbox{Tissue Ps with evol. comm. rules} & \verb=\TEC[\alpha]{\beta}= & \TEC[\alpha]{\beta} \\ + \mbox{Tissue Ps with evol. comm. and division rules} & \verb=\TDEC{\alpha}= & \TDEC{\alpha} \\ + \mbox{Tissue Ps with evol. comm. and separation rules} & \verb=\TSEC{\alpha}= & \TSEC{\alpha} \\ + \mbox{Ps with evol. comm. rules} & \verb=\CEC[\alpha]{\beta}= & \CEC[\alpha]{\beta} \\ + \mbox{Ps with evol. comm. and division rules} & \verb=\CDEC{\alpha}= & \CDEC{\alpha} \\ + \mbox{Ps with evol. comm. and separation rules} & \verb=\CSEC{\alpha}= & \CSEC{\alpha} +\end{array} +$ + +To define a new notation for a family of membrane systems, it is +enough to make a new command as follows: + +\begin{verbatim} +\newcommand{\MS}[3]{\Pfamily{MS}{#1}{#2}{#3}} +\end{verbatim} + +This results in: $\Pfamily{MS}{\#2}{\#3}{\#4}$. + +\subsection{Computational complexity theory} +\label{sec:comp-compl-theory} + +It is usual to define different complexity classes in the framework +of membrane computing. In this sense, it would be interesting to +automate the definition of these classes to avoid using all \LaTeX +commands each time we want to use them. + +$ +\begin{array}{lll} + \mbox{} & \verb=\PMC[\alpha]{\beta}= & \PMC[\alpha]{\beta} \\ + \mbox{} & \verb=\PSPACEMC[\alpha]{\beta}= & \PSPACEMC[\alpha]{\beta} \\ + \mbox{} & \verb=\EXPMC[\alpha]{\beta}= & \EXPMC[\alpha]{\beta} \\ + \mbox{} & \verb=\EXPSPACEMC[\alpha]{\beta}= & \EXPSPACEMC[\alpha]{\beta} \\ +\end{array} +$ + +To define a new notation for a complexity class in membrane systems, it is +enough to make a new command as follows: + +\begin{verbatim} +\newcommand{\C}[3]{\complClass{C}{#1}{#2}} +\end{verbatim} + +This results in: $\complClass{C}{\#1}{\#2}$~\footnote{CMC does not + stand for Conference on Membrane Computing here.}. + +\subsection{P systems} +\label{sec:p-systems} + +One of the two main contributions of this package is to make easier to +name a P system. Usually, when we have to define a new membrane +system, we have to write something like + +\begin{verbatim} +\Pi = (\Gamma, \mu, H, \mathcal{M}_1, \mathcal{M}_{2}, \mathcal{R}, i_{out}) +\end{verbatim} + +For making this task easier, the command \verb=psystem= has been +defined. Basically, it takes 5 arguments (first is optional) and can +be used as follows: \verb=\psystem[#1]{#2}{#3}{#4}{#5}=, where + +\begin{enumerate}[label=\texttt{\#\arabic*}] +\item $\in \{\mathtt{recognizer}, \mathtt{nonrecognizer}\}$: adds an + input alphabet and an input region. +\item $\in \{\mathtt{cell}, \mathtt{tissue}\}$: adds a membrane + structure in the first case. +\item + $\in \{\mathtt{transition}, \mathtt{activemembranes}, + \mathtt{symportantiport}, \mathtt{spiking}, \mathtt{kernel}, + \mathtt{colony}\}$: changes some of the parameters of the P system. +\item is a subscript for the symbol $\Pi$. +\item $> 1$ is the degree of the system. +\end{enumerate} + +For instance, the command +\begin{verbatim} +\psystem[recognizer]{cell}{activemembranes}{1}{10} +\end{verbatim} +would lead to the following: + +\begin{center} + \psystem[recognizer]{cell}{activemembranes}{1}{10} +\end{center} + +Some templates have been prepared for most of the usual variants of P +systems: + +$ +\begin{array}{ll} + \verb=\psystemAM= & \psystemAM \\ + \verb=\rpsystemAM= & \rpsystemAM \\ + \verb=\psystemSA= & \psystemSA \\ + \verb=\rpsystemSA= & \rpsystemSA \\ + \verb=\SNpsystem= & \SNpsystem \\ + \verb=\rSNpsystem= & \rSNpsystem \\ + \verb=\kpsystem= & \kpsystem \\ + \verb=\rkpsystem= & \rkpsystem \\ + \verb=\pcolony= & \pcolony \\ + \verb=\rpcolony= & \rpcolony \\ +\end{array} +$ + +All commands preceded by a \verb=r= are the recognizer version of +their r-less counterpart. + +\subsection{Rules} +\label{sec:rules} + +The (current) big work of this paper is to normalise the notation of +the rules of P systems. Several differences can be found in the +literature, most of them about spacing, position of elements, and so +on. The idea is to unify these notations in one big element: the +\verb=\mcrule= command. This command tries to cover all types of rules +in the membrane computing framework, including esoteric rules that +could arise. The idea is to catch some basic elements and parse them +in order to obtain the whole rule. As some types of P systems use +different notations, as arrows, separators and so on, different cases +have being contemplated. The definition of this command is +\verb=\mcrule[#1]{#2}{#3}{#4}{#5}{#6}=, where: + +\begin{enumerate}[label=\texttt{\#\arabic*}] +\item $\in \{\mathtt{written} (\mathit{Default}), \mathtt{plingua}\}$: the first one + makes it look as the usual scientific notation while the second one + transforms the rule into P-Lingua notation. +\item It can be one of the following parameters: + + $ + \begin{array}{lll} + \mathtt{rewriting} & \mbox{Classical rewriting rules} & \rewritingT \\ + \mathtt{single} & \mbox{Rules with a single pair of brackets} & \pevolutionT \\ + \mathtt{multiple} & \mbox{Rules with different brackets in the LHS and the RHS} & \psendoutT \\ + \mathtt{paren} & \mbox{Rules delimited by parentheses} & \antiportT \\ + \mathtt{spike} & \mbox{Spiking rules} & \spikingT + \end{array} +$ +\item $> 1$: Number of regions in the LHS (the main region and the outside regions are counted as one) +\item $> 1$: Number of regions in the RHS (the main region and the outside regions are counted as one) +\item explained below +\item explained below +\end{enumerate} + +The \verb=\mcrule= command is a tool capable of representing a wide +variety of types of rule. The idea is to represent all the rules in a +standardised way and well-spaced. An example with each type of rule is +given: + +\begin{itemize} +\item $\mathtt{rewriting}$: \verb=\mcrule{rewriting}{}{}{u}{v}= will + produce $\mcrule{rewriting}{}{}{u}{v}$. +\item $\mathtt{single}$: + \verb=\mcrule{single}{}{}{{a}{h}{+}}{{c_{2}\alpha}}= will produce + $\mcrule{single}{}{}{{a}{h}{+}}{c_{2}\alpha}$. +\item $\mathtt{multiple}$:\newline + \verb=\mcrule{multiple}{4}{4}{{{a}{3}{+}}{{b}}{{e_{1}}{4}}{;}}=\newline + \verb={{}{{a}}{-}{{o}{!}}}= will produce\newline + $\mcrule{multiple}{4}{4}{{{a}{3}{+}}{{b}}{{e_{1}}{4}}{;}}{{}{{a}}{-}{{o}{!}}}$. I + will explain in detail what means each thing: + \begin{itemize} + \item \verb={4}{4}=: In the left-hand side of the rule, 4 + ``regions'' will be analysed (in this case, membrane $3$, its + parent membrane, membrane $4$ and a special symbol); In the + right-hand side of the rule, 4 ``regions'' will be analysed (in + this case, the empty ``main'' membrane, its parent membrane, a + special symbol and a special region)~\footnote{It is a very + strange rule, but it will be useful to explain some special + cases to use in your own rules.}. + \item \verb={{{a}{3}{+}}{{b}}{{e_{1}}{4}}{;}}=: It is divided into + four parts: + \begin{itemize} + \item \verb={{a}{3}{+}}=: The ``main'' membrane of the rule has + label $3$ and polarisation $+$, and its contents is an object + $a$. + \item \verb={{b}}=: The outer content of the ``main'' membrane is + an object $b$. + \item \verb={{e_{1}}{4}}=: It has a inner membrane with label $4$ + and its contents is an object $e_{1}$. + \item \verb={;}=: It writes down a $;$ symbol~\footnote{Useful for + creation/deletion rules in kP systems.}. + \end{itemize} + \item \verb={{}{{a}}{-}{{o}{!}}}=: It is divided into four + parts: + \begin{itemize} + \item \verb={}=: The ``main'' membrane of the rule is not + specified, so it is omitted~\footnote{Useful for dissolution + rules.}. + \item \verb={{a}}=: The outer content of the ``main'' membrane is + an object $a$. + \item \verb=-= It writes down a $-$ symbol~\footnote{Also useful + for creation/deletion rules in kP systems.}. + \item \verb={{o}{!}}=: The symbol $!$ in the label is a reserved + character to write down a guard $\{ o \}$~\footnote{Also used in + kP systems.}. + \end{itemize} + \end{itemize} +\item $\mathtt{paren}$: \verb=\mcrule{paren}{}{}{{ab}{3}}{{c}{2}}= + will produce $\mcrule{paren}{}{}{{ab}{3}}{{c}{2}}$. +\item $\mathtt{spike}$: + \verb=\mcrule{spike}{}{}{{a^{3}}{a^{2}}}{{a}{1}}= will produce + $\mcrule{spike}{}{}{{a^{3}}{a^{2}}}{{a}{1}}$. +\end{itemize} + +Using $\mathtt{plingua}$ instead of +$\mathtt{written}$ as the optional parameter, it will write the rule +in the P-Lingua syntax. Therefore, the $\mathtt{multiple}$ rule +previously used in this section would render as\newline +$\mcrule[plingua]{multiple}{4}{4}{{{a}{3}{+}}{{b}}{{e_{1}}{4}}{;}}{{}{{a}}{-}{{o}{!}}}$. + +With this, anyone can create almost any kind of rule that one could +think~\footnote{Do you have any idea about other kind of rule? Please + write me so I can think in a way to implement it.}. However, for the +sake of simplicity, I have defined some commands for the basic types +of rules from the bibliography. + +{\footnotesize +\begin{longtable}{ll} + \verb=\rewriting{u}{v}= & $\rewriting{u}{v}$ \\ + \verb=\rewritingT= & $\rewritingT$ \\ + \verb=\evolution{a}{b}{h}{\alpha}= & $\evolution{a}{b}{h}{\alpha}$ \\ + \verb=\evolutionT= & $\evolutionT$ \\ + \verb=\evolutionP{a}{b}{h}{\alpha}= & $\evolutionP{a}{b}{h}{\alpha}$ \\ + \verb=\evolutionPT= & $\evolutionPT$ \\ + \verb=\pevolution{a}{b}{h}= & $\pevolution{a}{b}{h}$ \\ + \verb=\pevolutionT= & $\pevolutionT$ \\ + \verb=\pevolutionP{a}{b}{h}= & $\pevolutionP{a}{b}{h}$ \\ + \verb=\pevolutionPT= & $\pevolutionPT$ \\ + \verb=\antiport{u}{i}{v}{j}= & $\antiport{u}{i}{v}{j}$ \\ + \verb=\antiportT= & $\antiportT$ \\ + \verb=\symportT= & $\symportT$ \\ + \verb=\antiportP{u}{i}{v}{j}= & $\antiportP{u}{i}{v}{j}$ \\ + \verb=\antiportPT= & $\antiportPT$ \\ + \verb=\symportPT= & $\symportPT$ \\ + \verb=\sendin{a}{b}{h}{\alpha_{1}}{\alpha_{2}}= & $\sendin{a}{b}{h}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\sendinT= & $\sendinT$ \\ + \verb=\sendinP{a}{b}{h}{\alpha_{1}}{\alpha_{2}}= & $\sendinP{a}{b}{h}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\sendinPT= & $\sendinPT$ \\ + \verb=\psendin{a}{b}{h}= & $\psendin{a}{b}{h}$ \\ + \verb=\psendinT= & $\psendinT$ \\ + \verb=\psendinP{a}{b}{h}= & $\psendinP{a}{b}{h}$ \\ + \verb=\psendinPT= & $\psendinPT$ \\ + \verb=\sendout{a}{b}{h}{\alpha_{1}}{\alpha_{2}}= & $\sendout{a}{b}{h}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\sendoutT= & $\sendoutT$ \\ + \verb=\sendoutP{a}{b}{h}{\alpha_{1}}{\alpha_{2}}= & $\sendoutP{a}{b}{h}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\sendoutPT= & $\sendoutPT$ \\ + \verb=\psendout{a}{b}{h}= & $\psendout{a}{b}{h}$ \\ + \verb=\psendoutT= & $\psendoutT$ \\ + \verb=\psendoutP{a}{b}{h}= & $\psendoutP{a}{b}{h}$ \\ + \verb=\psendoutPT= & $\psendoutPT$ \\ + \verb=\dissolution{a}{b}{h}{\alpha}= & $\dissolution{a}{b}{h}{\alpha}$ \\ + \verb=\dissolutionT= & $\dissolutionT$ \\ + \verb=\dissolutionP{a}{b}{h}{\alpha}= & $\dissolutionP{a}{b}{h}{\alpha}$ \\ + \verb=\dissolutionPT= & $\dissolutionPT$ \\ + \verb=\pdissolution{a}{b}{h}= & $\pdissolution{a}{b}{h}$ \\ + \verb=\pdissolutionT= & $\pdissolutionT$ \\ + \verb=\pdissolutionP{a}{b}{h}= & $\pdissolutionP{a}{b}{h}$ \\ + \verb=\pdissolutionPT= & $\pdissolutionPT$ \\ + \verb=\division{a}{b}{c}{h}{\alpha}{\alpha_{1}}{\alpha_{2}}= & $\division{a}{b}{c}{h}{\alpha}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\divisionT= & $\divisionT$ \\ + \verb=\divisionP{a}{b}{c}{h}{\alpha}{\alpha_{1}}{\alpha_{2}}= & $\divisionP{a}{b}{c}{h}{\alpha}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\divisionPT= & $\divisionPT$ \\ + \verb=\pdivision{a}{b}{c}{h}= & $\pdivision{a}{b}{c}{h}$ \\ + \verb=\pdivisionT= & $\pdivisionT$ \\ + \verb=\pdivisionP{a}{b}{c}{h}= & $\pdivisionP{a}{b}{c}{h}$ \\ + \verb=\pdivisionPT= & $\pdivisionPT$ \\ + \verb=\separation{a}{h}{\alpha}{\alpha_{1}}{\alpha_{2}}= & $\separation{a}{h}{\alpha}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\separationT= & $\separationT$ \\ + \verb=\separationP{a}{h}{\alpha}{\alpha_{1}}{\alpha_{2}}= & $\separationP{a}{h}{\alpha}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\separationPT= & $\separationPT$ \\ + \verb=\pseparation{a}{h}= & $\pseparation{a}{h}$ \\ + \verb=\pseparationT= & $\pseparationT$ \\ + \verb=\pseparationP{a}{h}= & $\pseparationP{a}{h}$ \\ + \verb=\pseparationPT= & $\pseparationPT$ \\ + \verb=\creation{a}{b}{c}{h}{h_{1}}{\alpha}{\alpha_{1}}{\alpha_{2}}= & $\creation{a}{b}{c}{h}{h_{1}}{\alpha}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\creationT= & $\creationT$ \\ + \verb=\creationP{a}{b}{c}{h}{h_{1}}{\alpha}{\alpha_{1}}{\alpha_{2}}= & $\creationP{a}{b}{c}{h}{h_{1}}{\alpha}{\alpha_{1}}{\alpha_{2}}$ \\ + \verb=\creationPT= & $\creationPT$ \\ + \verb=\pcreation{a}{b}{c}{h}{h_{1}}= & $\pcreation{a}{b}{c}{h}{h_{1}}$ \\ + \verb=\pcreationT= & $\pcreationT$ \\ + \verb=\pcreationP{a}{b}{c}{h}{h_{1}}= & $\pcreationP{a}{b}{c}{h}{h_{1}}$ \\ + \verb=\pcreationPT= & $\pcreationPT$ \\ + \verb=\spiking{E}{a^{n}}{a}{d}= & $\spiking{E}{a^{n}}{a}{d}$ \\ + \verb=\spikingT= & $\spikingT$ \\ + \verb=\forgettingT= & $\forgettingT$ \\ + \verb=\spikingP{E}{a^{n}}{a}{d}= & $\spikingP{E}{a^{n}}{a}{d}$ \\ + \verb=\spikingPT= & $\spikingPT$ \\ + \verb=\forgettingPT= & $\forgettingPT$ \\ + \verb=\krewriting{x}{y}{g}= & $\krewriting{x}{y}{g}$ \\ + \verb=\krewritingT= & $\krewritingT$ \\ + \verb=\krewritingP{x}{y}{g}= & $\krewritingP{x}{y}{g}$ \\ + \verb=\krewritingPT= & $\krewritingPT$ \\ + \verb=\linkcreation{x}{y}{t_{l_{i}}}{t_{l_{j}}}{g}= & $\linkcreation{x}{y}{t_{l_{i}}}{t_{l_{j}}}{g}$ \\ + \verb=\linkcreationT= & $\linkcreationT$ \\ + \verb=\linkcreationP{x}{y}{t_{l_{i}}}{t_{l_{j}}}{g}= & $\linkcreationP{x}{y}{t_{l_{i}}}{t_{l_{j}}}{g}$ \\ + \verb=\linkcreationPT= & $\linkcreationPT$ \\ + \verb=\linkdestruction{x}{y}{t_{l_{i}}}{t_{l_{j}}}{g}= & $\linkdestruction{x}{y}{t_{l_{i}}}{t_{l_{j}}}{g}$ \\ + \verb=\linkdestructionT= & $\linkdestructionT$ \\ + \verb=\linkdestructionP{x}{y}{t_{l_{i}}}{t_{l_{j}}}{g}= & $\linkdestructionP{x}{y}{t_{l_{i}}}{t_{l_{j}}}{g}$ \\ + \verb=\linkdestructionPT= & $\linkdestructionPT$ +\end{longtable} +} + +As you can see, the names follow a pattern: + +\begin{itemize} +\item Their name is descriptive in terms of the rule it represents. +\item If the rule starts with a \texttt{p}, it means that it is a + polarizationless rule. +\item If the rule ends with (or its second to last letter is) a + \texttt{P}, it means it will write the rule in P-Lingua format. +\item If the rule ends with a \texttt{T}, it means it is a rule + template; that is, the typical rule used to describe its behaviour. +\end{itemize} + +If you have an idea to make the notation simpler, please let me know. + +\section{Future work} +\label{sec:future-work} + +A TODO list for the future development of the package. Please do not +hesitate to contact me if you think that something should be included +in this list, or if there is any bug or concept that should be +included as soon as possible. Please, contact me at +\href{mailto:dorellana@us.es}{dorellana@us.es} + +\begin{itemize} +\item Add new variants of P systems, as well as some new templates for + other rules. +\item Clean the code and create new command for analysing the + \texttt{multiple} case automatically. +\item Add the possibility of define rules with more than one level of + deepness. +\item Add a automatic parsing of a membrane structure, so a + well-spaced structure can appear in a paper. It would be interesting + to also let it export a string in the P-Lingua format. +\item A long-term objective is to export a .pdf with the picture of a + P system with its contents. Creating an image for your paper could + be as simple as defining it as you usually do, it would be cool, right? +\end{itemize} + +I hope you find the package interesting and useful for your +purposes. And, as I said above, please do not hesitate to contact me +if you have any questions of or suggestions for it. + +\end{document} |