Re: [tlaplus] Modelling the Philosophers Dining Problem

[Stephan Merz <stephan.merz@xxxxxxxxx>]

Hello,

two quick remarks.

1. The definition of your next-state relation is

Next == \A p \in Range(Philosophers) : (StartEating(p) /\ StopEating(p)) \/ StartThinking(p)

This is saying that *all* philosophers move at every system transition. You certainly want to specify that *some* philosopher takes a move, so replace \A with \E.

Also, the body of that formula asserts that either a philosopher starts thinking or that she starts and stops eating simultaneously. Again, this is certainly wrong. One could imagine that thinking and eating alternate, so "start thinking" doesn't need to be a separate transition (because a philosopher starts thinking as soon as she stops eating), but starting and stopping eating should not occur simultaneously.

2. The real challenge in the problem is to avoid the deadlock situation that occurs when each philosopher holds one fork but cannot acquire the second one because it is held by her neighbor. You trivialized that problem by having each philosopher take up and lay down both forks simultaneously. The original formulation of the problem states that forks are taken up individually (see also [1]). This is what makes the problem interesting.

Stephan

[1] https://en.wikipedia.org/wiki/Dining_philosophers_problem

On 10 Feb 2021, at 14:32, Younes <younesagma@xxxxxxxxx> wrote:

Hi everyone,

I'm new to TLA+ and I'm trying to model the Philosophers Dining Problem.

My initial setup puts all philosophers into "thinking" and all forks to be "available".

I have a deadlock in my current model, and I think, it is because :

The Next action describes : the alternation (\/) of Thinking and Eating actions. This state of the system (all philosophers are thinking) can occur indefinitely.

How do I combine alternation of the actions (think & eat) in the system whilst avoiding a deadlock ? An intermediate state ? I'm confused.

Also, I will be grateful to take any remarks/comments about the design, or the approach. I am really looking forward into getting your critics / reviews.

TLA+ Source Code :

https://gist.github.com/YounesTea/35f52a52e50db114e18366bf73da564f#file-diningproblem-tla

Thank you all

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