From 171740efd6e1f85e0945b714f065a8fc5e85ede8 Mon Sep 17 00:00:00 2001 From: Claudio Maggioni Date: Thu, 11 May 2023 21:26:10 +0200 Subject: [PATCH] Report explains ProMeLa code and all LTLs --- ReversalModel/run.sh | 4 +- report.pdf | Bin 234579 -> 242680 bytes report.tex | 114 +++++++++++++++++++++++++++++++++++++------ 3 files changed, 102 insertions(+), 16 deletions(-) diff --git a/ReversalModel/run.sh b/ReversalModel/run.sh index a88a837..5f591df 100755 --- a/ReversalModel/run.sh +++ b/ReversalModel/run.sh @@ -6,7 +6,7 @@ SCRIPT_DIR=$(cd -- "$( dirname -- "${BASH_SOURCE[0]}" )" &> /dev/null && pwd) cc="gcc-13" -if [ "$#" -ne 54]; then +if [ "$#" -ne 4 ]; then echo "$0: [ltl-prop] [n] [length] [r]" > /dev/stderr exit 1 fi @@ -19,6 +19,8 @@ compile_dir="$(mktemp -d)" cp "$SCRIPT_DIR/reversal.pml.m4" "$compile_dir" cd "$compile_dir" +echo "Compiling in: $compile_dir" + m4 -DN="$2" -DLENGTH="$3" -DR="$4" -DLTL="$1" reversal.pml.m4 > "$filename" spin -a "$filename" "$cc" 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+\usepackage[margin=2cm,bottom=3cm]{geometry} \usepackage{hyperref} \usepackage{listings} \usepackage{xcolor} @@ -140,22 +140,25 @@ bool seq_eq_to_parallel = true; reverser store the reversed array. The \texttt{done} array stores an array of boolean values: \mintinline{c}{done[0]} stores whether the sequential reverser has terminated, and each \mintinline{c}{done[i]} for $1 \leq i \leq N$ stores -whether the i-th spawned thread of the parallel reverser has terminated -(consequently, since threads are joined in order, when \mintinline{c}{done[N] == true} the parallel reverser terminates). Finally +whether the i-th spawned thread of the parallel reverser has terminated. +Consequently, since threads are joined in order, when +\mintinline{c}{done[N] == true} the parallel reverser terminates, an effect that +is exploited by the main model body implementation to wait for it. Finally \texttt{seq\_eq\_to\_parallel} is set to \mintinline{c}{false} when an incongruence between \texttt{reversed\_seq} and \texttt{reversed\_par} is found -after termination of both reversers. +after termination of +both reversers. The body of the model is structured in the following way: -\begin{minted}{c} +\begin{minted}{kotlin} init { { /* array initialization */ } /* sequential reverser algorithm */ run SequentialReverser(); /* parallel reverser algorithm */ - run ParallelReverser() + run ParallelReverser(); (done[0] == true && done[N] == true); @@ -163,12 +166,16 @@ init { } \end{minted} -{\color{red}TODO: FIX EXPLAINATION TO REFLECT USE OF PROCTYPE} - Each of the enumerated sections is surrounded by curly braces to emulate the effect of locally scoped variables in procedures, which do not exist in \textit{ProMeLa} aside the concurrency emulating \texttt{proctype} construct. +As requested by the assignment, the sequential and parallel reverser are +implemented in a \texttt{proctype} and spawned in parallel in the model. The two +\textit{ProMeLa} processes join before the congruence check thanks to an +``expression'' statement waiting on the termination boolean array to signal that +both reversers have finished doing their job. + The array initialization is carried out as follows: \begin{minted}{c} @@ -281,20 +288,97 @@ it is declared and set to a meaningful value in this block of the model. In this section I cover the LTL property definitions I included in the model. -The following LTL property definition checks that once both reversers have -terminated, the content of - -\begin{minted}{c} +\begin{minted}{scala} ltl seq_eq_parallel { [] (seq_eq_to_parallel == true) } \end{minted} +This LTL property definition checks that once both reversers have terminated, +the content of the respective reversed arrays they produce is the same. As +discussed in the previous section, this variable can only turn to false during +the execution of the congruence check and only if a pair of array elements of +same index is indeed different. Therefore, if the program is correct, the value +of the variable will always be true. + +Note that this property does not ensure +termination of the program, at it relies on the congruence check to eventually +run at the end of the program. To ensure termination, I define the following LTL +property: + +\begin{minted}{scala} +ltl termination { + <> (done[0] == true && done[N] == true) +} +\end{minted} + +This mirrors the wait statement introduced in the model code before the +congruence check block, and relies exactly in the same way on the termination +boolean array. Note that the elements of the array can only turn from +\mintinline{c}{false} to \mintinline{c}{true} or not change at all, thus the +property in the ``eventually'' operator is actually always true after it becomes +indeed true (i.e.\ the program cannnot un-terminate according to the model). + +I then define other two custom properties showcasing the powers of the +M4 macro processor when compared to the built-in \textit{ProMeLa} one. + +\begin{minted}{scala} +// ifelse(LTL, correctness_seq, ` +ltl correctness_seq { + [] (done[0] == true -> (true for(`k', 0, LENGTH-1, ` && + r_s[eval(LENGTH - k - 1)] == a[k]'))) +} +// ', `') +\end{minted} + +This property checks if the array produced by the sequential reverser is indeed +the reverse of the input array. Note that the ``polyglot'' M4 sugar allows for +the property to be arbitrairly unraveled based on the value of \texttt{LENGTH}. +Notice that to simplify the \textit{ProMeLa} source code to compile for long +array lengths, thanks to the \texttt{ifelse} macro the property is omitted by M4 +when the property is not actually checked (because long LTL properties actually +make the model fail to parse). Here is an example of the unravelled property for +\mintinline{c}{LENGTH = 10}: + +\begin{minted}{scala} +ltl correctness_seq { + [] (done[0] == true -> (true && + r_s[9] == a[0] && + r_s[8] == a[1] && + r_s[7] == a[2] && + r_s[6] == a[3] && + r_s[5] == a[4] && + r_s[4] == a[5] && + r_s[3] == a[6] && + r_s[2] == a[7] && + r_s[1] == a[8] && + r_s[0] == a[9])) +} +\end{minted} + +Note that the use of \mintinline{c}{true} as the first condition after the +implication is simply to allow for \mintinline{c}{&&} to be simply appended at +the start of each condition. + +In a similar fashion, I also define a property that is not generally true. The +following LTL formula specifies that when the second thread of the parallel +reverser terminates, the section to be reversed by the first thread is already +reversed. + +\begin{minted}{scala} +// ifelse(LTL, correctness_par, ` +ltl correctness_par { + [] (done[2] == true -> (true for(`k', 0, LENGTH / N - 1, ` && + r_p[eval(LENGTH - k - 1)] == a[k]'))) +} +// ', `') +\end{minted} + +This property is clearly not generally true as the first thread may not complete +the reversal process before the second thread terminates due to concurrency. - - The citation \cite{tange_2023_7855617}. -The citation \cite{spin}. +The citation \cite{tange_2023_7855617}. \begin{figure}