From 2b04820abccb0772b10b2c53542ecddc6a6f600c Mon Sep 17 00:00:00 2001 From: =?utf8?q?Jean-Fran=C3=A7ois=20Couchot?= Date: Mon, 13 Apr 2015 16:20:10 +0200 Subject: [PATCH] fsfd --- annexePromelaProof.tex | 12 +- images/faig.dot | 30 ++ images/faig.pdf | Bin 0 -> 10928 bytes images/fgig.dot | 41 +++ images/fgig.pdf | Bin 0 -> 11498 bytes images/fsig.dot | 19 ++ images/fsig.pdf | Bin 0 -> 10213 bytes images/gf.dot | 10 + images/gf.pdf | Bin 0 -> 10858 bytes images/gfp.pdf | Bin 0 -> 10793 bytes main.glsdefs | 330 ------------------- main.pdf | Bin 1771828 -> 1826830 bytes main.tex | 32 +- mixage.tex | 64 ++-- modelchecking.tex | 15 +- plan.tex | 12 +- sdd.tex | 718 ++++++++++++++++++++++++++++++----------- 17 files changed, 701 insertions(+), 582 deletions(-) create mode 100644 images/faig.dot create mode 100644 images/faig.pdf create mode 100644 images/fgig.dot create mode 100644 images/fgig.pdf create mode 100644 images/fsig.dot create mode 100644 images/fsig.pdf create mode 100644 images/gf.dot create mode 100644 images/gf.pdf create mode 100644 images/gfp.pdf delete mode 100644 main.glsdefs diff --git a/annexePromelaProof.tex b/annexePromelaProof.tex index dbc5774..1f70e9f 100644 --- a/annexePromelaProof.tex +++ b/annexePromelaProof.tex @@ -228,11 +228,7 @@ to $F(Xd^{l+1}_{k\,0}, \ldots,Xd^{l+1}_{k\,n-1})$. Thanks to \end{Proof} -\begin{theorem}[Soundness wrt universal convergence property]\label{Theo:sound} - Let $\phi$ be a DDN model and $\psi$ be its translation. If $\psi$ verifies - the LTL property (\ref{eq:ltl:conv}) under weak fairness property, then - iterations of $\phi$ are universally convergent. -\end{theorem} +\promelasound* \begin{Proof} % For the case where the strategy is finite, one notice that property % verification is achieved under weak fairness property. Instructions that @@ -259,12 +255,8 @@ to $F(Xd^{l+1}_{k\,0}, \ldots,Xd^{l+1}_{k\,n-1})$. Thanks to % \end{Corol} +\promelacomplete* -\begin{theorem}[Completeness wrt universal convergence property]\label{Theo:completeness} - Let $\phi$ be a DDN model and $\psi$ be its translation. If $\psi$ does not - verify the LTL property (\ref{eq:ltl:conv}) under weak fairness property then - the iterations of $\phi$ are divergent. -\end{theorem} \begin{Proof} For models $\psi$ that do not verify the LTL property (\ref{eq:ltl:conv}) it is easy to construct corresponding iterations of the DDN, whose strategy is diff --git a/images/faig.dot b/images/faig.dot new file mode 100644 index 0000000..82fa8d8 --- /dev/null +++ b/images/faig.dot @@ -0,0 +1,30 @@ +digraph { +000 [shape="none"label="000", pos="10.5,10!",fontsize=20,fixedsize=true,width=0.5,height=0.3]; +001 [shape="none"label="001", pos="11.7320508076,11!",fontsize=20,fixedsize=true,width=0.5,height=0.3]; +010 [shape="none", label="010", pos="12.5,10!",fontsize=20,fixedsize=true,width=0.5,height=0.3]; +011 [shape="none", label="011", pos="13.7320508076,11!",fontsize=20,fixedsize=true,width=0.5,height=0.3]; +100 [shape="none", label="100", pos="10.5,8!",fontsize=20,fixedsize=true,width=0.5,height=0.3]; +101 [shape="none", 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IK?3l90LI+8$p8QV literal 0 HcmV?d00001 diff --git a/main.glsdefs b/main.glsdefs deleted file mode 100644 index 334ef46..0000000 --- a/main.glsdefs +++ /dev/null @@ -1,330 +0,0 @@ -\ifglsentryexists{graphoriente}{}% -{% -\gls@defglossaryentry{graphoriente}% -{% -name={graphe orienté},% -sort={graphe orienté},% -type={main},% -first={graphe orient\IeC {\'e}},% -firstplural={graphe orient\IeC {\'e}s},% -text={graphe orient\IeC {\'e}},% -plural={graphe orient\IeC {\'e}s},% -description={Un graphe orienté $G=(S,A)$ est défini par la donnée d'un ensemble de sommets $S$ et d'un ensemble d'arcs $A$, chaque arc étant représenté par un couple de sommets. Si $x$ et $y$ sont des sommets de $S$, le couple $(x,y)$ représente l'arc orienté allant du sommet \emph {origine} $x$ au sommet \emph {extremité} $y$.},% -descriptionplural={Un graphe orienté $G=(S,A)$ est défini par la donnée d'un ensemble de sommets $S$ et d'un ensemble d'arcs $A$, chaque arc étant représenté par un couple de sommets. Si $x$ et $y$ sont des sommets de $S$, le couple $(x,y)$ représente l'arc orienté allant du sommet \emph {origine} $x$ au sommet \emph {extremité} $y$.},% -symbol={\relax },% -symbolplural={\relax },% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{graphfortementconnexe}{}% -{% -\gls@defglossaryentry{graphfortementconnexe}% -{% -name={graphe fortement connexe},% -sort={graphe fortement connexe},% -type={main},% -first={graphe fortement connexe},% -firstplural={graphe fortement connexes},% -text={graphe fortement connexe},% -plural={graphe fortement connexes},% -description={Un graphe orienté $G=(S,A)$ est fortement connexe si pour tout couple de sommets $x$, $y$ de $S$ il existe un chemin reliant $x$ à $y$ et $y$ à $x$.},% -descriptionplural={Un graphe orienté $G=(S,A)$ est fortement connexe si pour tout couple de sommets $x$, $y$ de $S$ il existe un chemin reliant $x$ à $y$ et $y$ à $x$.},% -symbol={\relax },% -symbolplural={\relax },% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{distributionuniforme}{}% -{% -\gls@defglossaryentry{distributionuniforme}% -{% -name={distribution uniforme},% -sort={distribution uniforme},% -type={main},% -first={distribution uniforme},% -firstplural={distribution uniformes},% -text={distribution uniforme},% -plural={distribution uniformes},% -description={Les lois de distribution uniforme (ou loi uniformes continues) forment une famille de lois à densité caractérisées par la propriété suivante: tous les intervalles de même longueur inclus dans le support de la loi ont la même probabilité.},% -descriptionplural={Les lois de distribution uniforme (ou loi uniformes continues) forment une famille de lois à densité caractérisées par la propriété suivante: tous les intervalles de même longueur inclus dans le support de la loi ont la même probabilité.},% -symbol={\relax },% -symbolplural={\relax },% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{partieentiere}{}% -{% -\gls@defglossaryentry{partieentiere}% -{% -name={partie entière},% -sort={partie entière},% -type={main},% -first={partie enti\IeC {\`e}re},% -firstplural={partie enti\IeC {\`e}res},% -text={partie enti\IeC {\`e}re},% -plural={partie enti\IeC {\`e}res},% -description={La partie entière d'un nombre réel est l'entier qui lui est immédiatement inférieur ou égal. Pour un nombre réel $x$, on la note $\lfloor x \rfloor $.},% -descriptionplural={La partie entière d'un nombre réel est l'entier qui lui est immédiatement inférieur ou égal. Pour un nombre réel $x$, on la note $\lfloor x \rfloor $.},% -symbol={\ensuremath {\lfloor x \rfloor }},% -symbolplural={\ensuremath {\lfloor x \rfloor }},% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{distanceHamming}{}% -{% -\gls@defglossaryentry{distanceHamming}% -{% -name={distance de Hamming},% -sort={distance de Hamming},% -type={main},% -first={distance de Hamming},% -firstplural={distance de Hammings},% -text={distance de Hamming},% -plural={distance de Hammings},% -description={La distance de Hamming entre deux éléments $x=(x_1,\ldots ,x_n)$ et $y=(y_1,\ldots ,y_n)$ dans $\Bool ^n$ est le nombre d'indices $i$, $1 \le i \le n$ tels que $x_i$ diffère de $y_i$.},% -descriptionplural={La distance de Hamming entre deux éléments $x=(x_1,\ldots ,x_n)$ et $y=(y_1,\ldots ,y_n)$ dans $\Bool ^n$ est le nombre d'indices $i$, $1 \le i \le n$ tels que $x_i$ diffère de $y_i$.},% -symbol={\relax },% -symbolplural={\relax },% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{decalageDeBits}{}% -{% -\gls@defglossaryentry{decalageDeBits}% -{% -name={décalage de bits},% -sort={décalage de bits},% -type={main},% -first={d\IeC {\'e}calage de bits},% -firstplural={d\IeC {\'e}calages de bits},% -text={d\IeC {\'e}calage de bits},% -plural={d\IeC {\'e}calages de bits},% -description={Soit $x$ un nombre binaire de $n$ bits et $b$ un entier. Le nombre binaire de $n$ bits $x \ll b$ (respectivement $x \gg b$) est obtenu en décalant les bits de $x$ de $b$ bits vers la gauche (resp. vers la droite) et en complétant avec des zéros à droite (resp. à gauche).},% -descriptionplural={Soit $x$ un nombre binaire de $n$ bits et $b$ un entier. Le nombre binaire de $n$ bits $x \ll b$ (respectivement $x \gg b$) est obtenu en décalant les bits de $x$ de $b$ bits vers la gauche (resp. vers la droite) et en complétant avec des zéros à droite (resp. à gauche).},% -symbol={\relax },% -symbolplural={\relax },% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{chaineDeMarkov}{}% -{% -\gls@defglossaryentry{chaineDeMarkov}% -{% -name={chaîne de Markov},% -sort={chaîne de Markov},% -type={main},% -first={cha\IeC {\^\i }ne de Markov},% -firstplural={cha\IeC {\^\i }nes de Markov},% -text={cha\IeC {\^\i }ne de Markov},% -plural={cha\IeC {\^\i }nes de Markov},% -description={On se restreint à la définition d'une chaîne de Markov homogène. Celle-ci désigne une suite de variables aléatoires $(X_n)_{n \in \Nats }$ à temps discret, à espace d'états discret, sans mémoire et dont le mécanisme de transition ne change pas au cours du temps. Formellement la propriété suivante doit être établie:\newline $ \forall n \ge 0, \forall (i_0, \ldots , i_{n-1}, i,j),\\ \textrm { }P(X_{n+1}=j\mid X_0=i_0, X_1=i_1, X_2=i_2, \ldots , X_{n-1}=i_{n-1}, X_{n}=i) \\ \textrm { }= P(X_{1}=j\mid X_n=i). $},% -descriptionplural={On se restreint à la définition d'une chaîne de Markov homogène. Celle-ci désigne une suite de variables aléatoires $(X_n)_{n \in \Nats }$ à temps discret, à espace d'états discret, sans mémoire et dont le mécanisme de transition ne change pas au cours du temps. Formellement la propriété suivante doit être établie:\newline $ \forall n \ge 0, \forall (i_0, \ldots , i_{n-1}, i,j),\\ \textrm { }P(X_{n+1}=j\mid X_0=i_0, X_1=i_1, X_2=i_2, \ldots , X_{n-1}=i_{n-1}, X_{n}=i) \\ \textrm { }= P(X_{1}=j\mid X_n=i). $},% -symbol={\relax },% -symbolplural={\relax },% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{vecteurDeProbabilite}{}% -{% -\gls@defglossaryentry{vecteurDeProbabilite}% -{% -name={vecteur de probabilités},% -sort={vecteur de probabilités},% -type={main},% -first={vecteur de probabilit\IeC {\'e}s},% -firstplural={vecteurs de probabilit\IeC {\'e}s},% -text={vecteur de probabilit\IeC {\'e}s},% -plural={vecteurs de probabilit\IeC {\'e}s},% -description={Un vecteur de probabilités est un vecteur tel que toutes ses composantes sont positives ou nulles et leur somme vaut 1.},% -descriptionplural={Un vecteur de probabilités est un vecteur tel que toutes ses composantes sont positives ou nulles et leur somme vaut 1.},% -symbol={\relax },% -symbolplural={\relax },% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{matriceDAdjacence}{}% -{% -\gls@defglossaryentry{matriceDAdjacence}% -{% -name={matrice d'adjacence},% -sort={matrice d'adjacence},% -type={main},% -first={matrice d'adjacence},% -firstplural={matrice d'adjacences},% -text={matrice d'adjacence},% -plural={matrice d'adjacences},% -description={La matrice d'adjacence du graphe orienté $G=(S,A)$ à $n$ sommets est la matrice $\check {M}$ de dimension $n \times n$ dont l'élément $\check {M}_{ij}$ représente le nombre d'arcs d'origine $i$ et d'extrémité $j$.},% -descriptionplural={La matrice d'adjacence du graphe orienté $G=(S,A)$ à $n$ sommets est la matrice $\check {M}$ de dimension $n \times n$ dont l'élément $\check {M}_{ij}$ représente le nombre d'arcs d'origine $i$ et d'extrémité $j$.},% -symbol={\relax },% -symbolplural={\relax },% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{xor}{}% -{% -\gls@defglossaryentry{xor}% -{% -name={ou exclusif},% -sort={ou exclusif},% -type={main},% -first={ou exclusif},% -firstplural={ou exclusifs},% -text={ou exclusif},% -plural={ou exclusifs},% -description={La fonction \og ou exclusif\fg {}, XOR, est l'opérateur de $\Bool ^2$ dans $\Bool $ qui prend la valeur 1 si seulement si les deux opérandes ont des valeurs distinctes.},% -descriptionplural={La fonction \og ou exclusif\fg {}, XOR, est l'opérateur de $\Bool ^2$ dans $\Bool $ qui prend la valeur 1 si seulement si les deux opérandes ont des valeurs distinctes.},% -symbol={\ensuremath {\oplus }},% -symbolplural={\ensuremath {\oplus }},% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% -\ifglsentryexists{matriceDeTransitions}{}% -{% -\gls@defglossaryentry{matriceDeTransitions}% -{% -name={matrice de transitions},% -sort={matrice de transitions},% -type={main},% -first={matrice de transitions},% -firstplural={matrice de transitionss},% -text={matrice de transitions},% -plural={matrice de transitionss},% -description={Le nombre $p_{ij}= P(X_1=j \mid X_0 =i)$ est appelé probabilité de transition de l'état $i$ à l'état $j$ en un pas. La matrice composée des $p_{ij}$ est la matrice de transitions associée à la chaine de Markov $X$.},% -descriptionplural={Le nombre $p_{ij}= P(X_1=j \mid X_0 =i)$ est appelé probabilité de transition de l'état $i$ à l'état $j$ en un pas. La matrice composée des $p_{ij}$ est la matrice de transitions associée à la chaine de Markov $X$.},% -symbol={\relax },% -symbolplural={\relax },% -user1={},% -user2={},% -user3={},% -user4={},% -user5={},% -user6={},% -long={},% -longplural={},% -short={},% -shortplural={},% -counter={page},% -parent={},% -% -}% -}% diff --git a/main.pdf b/main.pdf index 5c4e3bd6ab43cffd20423f4a563c2d93d99b152b..5ee54b773f66abdba39983cc386dbb88660d4309 100644 GIT binary patch delta 282854 zcmZs?Ra9Kt(trz%yF0->xHRq%9D+-5cXvtSG#b2df&>p9+}$C#J0ZBcUG_fb-1|S= zhZ>{0YIe=4UOmSAR;^m~iS}__PS~`cr9QE6u<{_&PR;f&B6DzYLnzx2aB65Np^>;a zDcC8TOl^@NSj*_5NpaA^(Asj{0Gj`wkI=xRbKPVBkT2=n#0CIl|HlRZzPogj z0KDw)MxrD#GgSaDXOfEK`ZL3|gacR_BnX+!Dz0mH%fZ>a#jf09oE@bN@Qqr$xle4{if!mb1~GK75> zodP1Sf`AGD0wE?9=!~GBIxCJVe3$`u+G8sXUGsmkx2dcX6i9IY(#k$gtrcNJjnOdK z50@(>Jip|a*pId^$u(G8#4=2zr*m-?63PWLGpfW@W)g-jUgwJo)8~S zBtVznSmGKl%ONYr8Y>`UA)c$T*Y2jV&J{nK#hHd7>{rJ7kl58;3MphlBGipc1Xi#=%3oZl20Pm%)afv&+6QV#}TnbKsNKMsF~mB|?B!kN>+1zXxu!v5higQgR5 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