From fac84dbab33ac88320f37ae9d1b4362d8257c096 Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Tue, 1 Apr 2014 14:44:24 +0200 Subject: [PATCH] =?UTF-8?q?First-=20und=20Follow=20hinzugef=C3=BCgt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../Programmierparadigmen/Compilerbau.tex | 73 ++++++++++++++++++ documents/Programmierparadigmen/MPI.tex | 5 +- .../Programmierparadigmen.pdf | Bin 874315 -> 884271 bytes .../scripts/mpi/mpi-mybroadcast.c | 18 +++++ documents/Programmierparadigmen/shortcuts.sty | 2 + 5 files changed, 97 insertions(+), 1 deletion(-) create mode 100644 documents/Programmierparadigmen/scripts/mpi/mpi-mybroadcast.c diff --git a/documents/Programmierparadigmen/Compilerbau.tex b/documents/Programmierparadigmen/Compilerbau.tex index 6aa3dbe..2946226 100644 --- a/documents/Programmierparadigmen/Compilerbau.tex +++ b/documents/Programmierparadigmen/Compilerbau.tex @@ -184,6 +184,79 @@ Maschinencode oder Assembler zu erstellen. Dabei muss folgendes beachtet werden: \item \textbf{Nachoptimierung}\todo{?} \end{itemize} +\section{Weiteres} +\subsection{First- und Follow} +\begin{definition}[$k$-Präfix]\xindex{Präfix}\xindex{\# (Compilerbau)}% + Sei $G = (\Sigma, V, P, S)$ eine Grammatik, $k \in \mdn_{> 0}$ und + $x \in (V \cup \Sigma)^*$ mit + \[x = x_1 \dots x_m \text{ mit } x_i \in (V \cup \Sigma) \text{ wobei } i \in 1, \dots, m\] + + Dann heißt $\tilde{x} \in (V \cup \Sigma \cup \Set{\#})^+$ ein $k$-\textbf{Präfix} von $x$, + wenn gilt: + \[\tilde{x} = + \begin{cases} + x\# &\text{falls } x = x_1 \dots x_m \text{ und } m < k\\ + x_1 \dots x_k &\text{sonst} + \end{cases}\] + wobei $\#$ das Ende der Eingabe bezeichnet. In diesem Fall schreibt man + \[ \tilde{x} = k\ :\ x\] +\end{definition} + +\begin{beispiel}[$k$-Präfixe] + Sei $G = (\Set{A, B, C, S}, \Set{a, b, c}, P, S)$ mit + \begin{align*} + P = \{ &A \rightarrow aa | ab, \\ + &B \rightarrow AC,\\ + &C \rightarrow c,\\ + &S \rightarrow ABC\} + \end{align*} + + Dann gilt: + \begin{bspenum} + \item $A = 1 : S$ + \item $a = 1 : S$ + \end{bspenum} + + \todo[inline]{Das ist ein Problem! Damit wäre $k : x$ nicht wohldefiniert!} +\end{beispiel} + +\begin{definition}[First- und Follow-Menge]\xindex{Firstkx@$\text{First}_k(x)$}\xindex{Followkx@$\text{Follow}_k(x)$}% + Sei $G = (\Sigma, V, P, S)$ eine Grammatik und $x \in V$. + + \begin{defenum} + \item $\begin{aligned}[t]\First_k (x) := \{u \in (V \cup \Sigma)^+ | &\exists y \in \Sigma^*:\\ + &x \Rightarrow^* y\\ + \land &u = k : y \}\end{aligned}$ + \item $\begin{aligned}[t]\Follow_k(x) := \{u \in (V \cup \Sigma)^+ | &\exists m, y \in (V \cup \Sigma)^* :\\ + &S \Rightarrow^* mxy\\ + \land &u \in \First_k(y)\}\end{aligned}$ + \end{defenum} +\end{definition} + +\begin{beispiel}[First- und Follow-Mengen\footnotemark] + Sei $G = (\Sigma, V, P, E)$ mit + \begin{align*} + \Sigma &= \Set{+, *, (, )}\\ + V &= \Set{T, T', E, E', F}\\ + P &= \{ E \rightarrow T E'\\ + &\hphantom{= \{ } E' \rightarrow \varepsilon | +TE'\\ + &\hphantom{= \{ } T \rightarrow FT'\\ + &\hphantom{= \{ } T' \rightarrow \varepsilon | *FT'\\ + &\hphantom{= \{ } F \rightarrow \id | (E)\} + \end{align*} + + Dann gilt: + \begin{bspenum} + \item $\First(E) = \First(T) = \First(F) = \Set{\id, (\ )}$ + \item $\First(E') = \Set{\#, +}$ + \item $\First(T') = \Set{\#, *}$ + \item $\Follow(E) = \Follow(E') = \Set{\#, )}$ + \item $\Follow(T) = \Follow(T') = \Set{\#, ), +}$ + \item $\Follow(F) = \Set{\#, ), +, *}$ + \end{bspenum} +\end{beispiel} +\footnotetext{Folie 348} + \section{Literatur} Ich kann das folgende Buch empfehlen: diff --git a/documents/Programmierparadigmen/MPI.tex b/documents/Programmierparadigmen/MPI.tex index 59f56b1..6b6f7c8 100644 --- a/documents/Programmierparadigmen/MPI.tex +++ b/documents/Programmierparadigmen/MPI.tex @@ -172,9 +172,12 @@ Verteilt Daten vom Prozess \texttt{root} unter alle anderen Prozesse in der Grup \inputminted[numbersep=5pt, tabsize=4]{c}{scripts/mpi/mpi-reduce-example.c} \section{Beispiele} - +\subsection{sum-reduce Implementierung} \inputminted[numbersep=5pt, tabsize=4]{c}{scripts/mpi/mpi-sum-reduce.c} +\subsection[broadcast Implementierung]{broadcast Implementierung\footnote{Klausur WS 2012 / 2013}} +\inputminted[numbersep=5pt, tabsize=4]{c}{scripts/mpi/mpi-mybroadcast.c} + \section{Weitere Informationen} \begin{itemize} \item \url{http://mpitutorial.com/} diff --git a/documents/Programmierparadigmen/Programmierparadigmen.pdf b/documents/Programmierparadigmen/Programmierparadigmen.pdf index 1a5d4cf1ee8b12cd14b13728e2a43e9d180a96d1..f1e2129f402733d1b792570723a6953a5829bd70 100644 GIT binary patch delta 188829 zcmZs?b8sfn*EO0awr$&)*tRjTZB3j!v29H=*Zx;zl(oeGz$~- z3e81zPH>616;%mX^Y(N*G;2wRX*we|Hy(D5WW0oujmY6}Kbzvj3GI)rMdyzU#E;cl z5#Z2yz~aq+*0u>Pi#aDIU__OW;Q23*!2`dKR{4#B_54k91CqM zxdXY2KpSMy7SeU;BZT#zmXZNZ(da)xpVq_*0T=1)o{lU9lmVWT#AvM}(Lm6TRS`j9 zT3aL*!{#t-W*vHOu2IW}l(3-6n6o`%8w(HYf%B4oNW_b4v^-dHyOO5Vr#9*i)cnSk zZe_d0QjR%{zEZyjSiE4v^I7(#v~Z^5HCO!W=kgMr&3)SA@zi+;OAY+zYNKBM#ZyV~ zW&7j36}kmjppZ!`$LtNKpL)w^oG;By&Gd%N@!=(fVG9M(qrRn{V- 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