From 1e25f0d9d134f5a4afabdb87069d1fedb9c1ae06 Mon Sep 17 00:00:00 2001 From: Claudio Maggioni Date: Wed, 10 May 2023 16:47:52 +0200 Subject: [PATCH] promela expl done (minus ltl) --- report.pdf | Bin 222439 -> 232923 bytes report.tex | 113 ++++++++++++++++++++++++++++++++++++++++++++++++++++- 2 files changed, 112 insertions(+), 1 deletion(-) diff --git a/report.pdf b/report.pdf index 0a3acaf9baabe31eb1dbf510170660801310a975..ec45d7f3238880017377380decb33d021a3f66f9 100644 GIT binary patch delta 161584 zcmZUZLwKMKu%%XYOitwW!)wy>-qx8AII2 zMylV11!Lt(MEwEI$<2~(Ob<>CTPlDVF&mcbsLVpfP=YtQy*H9-|`?zw+g>s%WX7;wB zCWG>)aJsG8F4)9M?WRZPM0_is=Fd{|~tjq~c zn5mkC{f-GrlyQ;2n_j`fnt!V%X_S?E{ZYs=ptj0zZABrhh5*xI1}%rtEwfL?A6d3e znZgoHD!?Lja^h1?qj0q_7eA$ukoK?Y>i zK*;zIUxW`U{rSlTl%9&Z3K%le{XQ*J7?;nIaz~>Z#417NW{%QuUGlyBhd>U7e?cVF z(~lYt-(y~8nF`Jl5n!8gC> zEp|0xC3HdKz1wF!z%QP%~iG>meYaeaJjo$V!g#r9}emxN)J?m4JX=z9Z3`&DNncgw%h>ruoBcS(B}R_i50< z?&aW7xv#Ge7QSg>3mK==@+;-^v)rf7hZAc$%{*+rpIxZXQwER3LFU2)Jz(#;U%|hy 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follows: + +\begin{minted}{c} +int i; +for (i in to_reverse) { + int value; + select(value: 0 .. R); + to_reverse[i] = value; + printf("to_reverse[%d]: %d\n", i, value); +} +\end{minted} + +As specified above, the array is initialized with values in $[0,R]$. +Specifically, values are generated using a nondeterministic \texttt{select} +statement to allow the model checker to try all possible values efficiently. + +The sequential reversed algorithm is implemented with the following code: + +\begin{minted}{c} +int k; +for (k: 0 .. (LENGTH - 1)) { + reversed_seq[LENGTH - k - 1] = to_reverse[k]; + printf("reversed_seq[%d] = to_reverse[%d]\n", LENGTH - k - 1, k); +} +done[0] = true; +\end{minted} + +which is a direct translation of the Java implementation to verify. + +The sequential reverser is used to implement each thread of the parallel +reverser through the \textit{ThreadedReverser} class. In the model, the class is +translated in a Spin process through the \texttt{proctype} construct with the +following implementation: + +\begin{minted}{c} +proctype ThreadedReverser(int from; int to; int n) { + printf("proc[%d]: started from=%d to=%d\n", n, from, to); + int k; + for (k: from .. (to - 1)) { + printf("reversed_par[%d] = to_reverse[%d]\n", LENGTH - k - 1, k); + reversed_par[LENGTH - k - 1] = to_reverse[k]; + } + printf("proc[%d]: ended\n", n); + done[n] = true; +} +\end{minted} + +The implementation is closely related to the sequential one, as it differs only +in \texttt{reversed\_par} being used as the destination array and limiting the +reversal between \texttt{from} and \texttt{to}. The argument \texttt{n} is used +to identify the thread in the \texttt{done} array to store the termination +state. Following the indexing rules of \texttt{done} given earlier, the i-th +spawned thread corresponds to a \texttt{proctype} call with $n = i$, so that at +termination \mintinline{c}{done[i]} is set to \mintinline{c}{true}. + +The actual thread-spawning part of the parallel reverser, i.e.\ class +\textit{ParallelReverser} itself, is represented by the following +\textit{ProMeLa} code placed in the \texttt{init} section of the model: + +\begin{minted}{c} +int n; +int s = LENGTH / N; +for (n: 0 .. (N - 1)) { // fork loop + int from = n * s; + int to; + if + :: (n == N - 1) -> to = LENGTH; + :: else -> to = n * s + s; + fi + run ThreadedReverser(from, to, n + 1); // fork here +} +for (n: 1 .. N) { // join loop + (done[n] == true); // join n-th thread here + printf("[%d] joined\n", n); +} +\end{minted} + +Here the values of \texttt{n}, \texttt{s}, \texttt{from} and \texttt{to} +replicate exactly the values used in the Java implementation. The \texttt{n + 1} +parameter identifies maps each \texttt{proctype} invocation to its place in the +invocation order (e.g.\ for $n=0$, \texttt{ThreadedReverser} is called with +$n+1=1$, since this is the 1st invocation of the process). + +The second ``join'' loop waits for each process to complete in order of +invocation, replication the thread joining behaviour of the parallel reverser +implementation in the Java program. Note that the \textit{ProMeLa} statement +\mintinline{c}{(done[n] == true);} will ``wait'' for the value of +\mintinline{c}{done[n]} to be \mintinline{c}{true} before executing the +following statement, thus being an adequate analogy for +\mintinline{java}{Thread.join()}. + +Finally, the congruence check between the arrays produced by both implementation +is implemented with the following code: + +\begin{minted}{c} +int i; +for (i: 0 .. (LENGTH - 1)) { + if + :: (reversed_seq[i] != reversed_par[i]) -> seq_eq_to_parallel = false; + fi +} +\end{minted} + +Should any matching pair of elements be different, +\texttt{seq\_eq\_to\_parallel} will be set to \mintinline{c}{false}. Note that +this boolean variable is used to implement one of the LTL properties, hence why +it is declared and set to a meaningful value in this block of the model. + +\subsection{LTL properties} + The citation \cite{tange_2023_7855617}. The citation \cite{spin}.