Hello,
Read this:
Yet more precision about the invariants of a system..
I was just thinking about Petri nets , and i have studied more
Petri nets, they are useful for parallel programming, and
what i have noticed by studying them, is that there is two methods
to prove that there is no deadlock in the system, there is the
structural analysis with place invariants that you have to
mathematically find, or you can use the reachability tree, but we have
to notice that the structural analysis of Petri nets learns you more,
because it permits you to prove that there is no deadlock in the system,
and the place invariants are mathematically calculated by the following
system of the given Petri net:
Transpose(vector) * Incidence matrix = 0
So you apply the Gaussian Elimination or the Farkas algorithm to
the incidence matrix to find the Place invariants, and as you will
notice those place invariants calculations of the Petri nets look
like Markov chains in mathematics, with there vector of probabilities
and there transition matrix of probabilities, and you can, using
Markov chains mathematically calculate where the vector of probabilities
will "stabilize", and it gives you a very important information, and
you can do it by solving the following mathematical system:
Unknown vector1 of probabilities * transition matrix of probabilities =
Unknown vector1 of probabilities.
Solving this system of equations is very important in economics and
other fields, and you can notice that it is like calculating the
invariants , because the invariant in the system above is the
vector1 of probabilities that is obtained, and this invariant,
like in the invariants of the structural analysis of Petri nets,
gives you a very important information about the system, like where
market shares will stabilize that is calculated this way in economics.
About reachability analysis of a Petri net..
As you have noticed in my Petri nets tutorial example (read below),
i am analysing the liveness of the Petri net, because there is a rule
that says:
If a Petri net is live, that means that it is deadlock-free.
Because reachability analysis of a Petri net with Tina
gives you the necessary information about boundedness and liveness
of the Petri net. So if it gives you that the Petri net is "live" , so
there is no deadlock in it.
Tina and Partial order reduction techniques..
With the advancement of computer technology, highly concurrent systems
are being developed. The verification of such systems is a challenging
task, as their state space grows exponentially with the number of
processes. Partial order reduction is an effective technique to address
this problem. It relies on the observation that the effect of executing transitions concurrently is often independent of their ordering.
Tina is using “partial-order” reduction techniques aimed at preventing combinatorial explosion, Read more here to notice it:
http://projects.laas.fr/tina/papers/qest06.pdf
About modelizations and detection of race conditions and deadlocks
in parallel programming..
I have just taken further a look at the following project in Delphi
called DelphiConcurrent by an engineer called Moualek Adlene from France:
https://github.com/moualek-adlene/DelphiConcurrent/blob/master/DelphiConcurrent.pas
And i have just taken a look at the following webpage of Dr Dobb's journal:
Detecting Deadlocks in C++ Using a Locks Monitor
https://www.drdobbs.com/detecting-deadlocks-in-c-using-a-locks-m/184416644
And i think that both of them are using technics that are not as good
as analysing deadlocks with Petri Nets in parallel applications ,
for example the above two methods are only addressing locks or mutexes
or reader-writer locks , but they are not addressing semaphores
or event objects and such other synchronization objects, so they
are not good, this is why i have written a tutorial that shows my
methodology of analysing and detecting deadlocks in parallel
applications with Petri Nets, my methodology is more sophisticated
because it is a generalization and it modelizes with Petri Nets the
broader range of synchronization objects, and in my tutorial i will add
soon other synchronization objects, you have to look at it, here it is:
https://sites.google.com/site/scalable68/how-to-analyse-parallel-applications-with-petri-nets
You have to get the powerful Tina software to run my Petri Net examples
inside my tutorial, here is the powerful Tina software:
http://projects.laas.fr/tina/
Also to detect race conditions in parallel programming you have to take
a look at the following new tutorial that uses the powerful Spin tool:
https://mirrors.edge.kernel.org/pub/linux/kernel/people/paulmck/perfbook/perfbook.html
This is how you will get much more professional at detecting deadlocks
and race conditions in parallel programming.
Thank you,
Amine Moulay Ramdane.
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)