How to model check this "real-time" spec?

[ns]

hello I've been reading the chapter on Real-time in the Specifying Systems book and am trying to experiment with a small spec that uses an integer clock (thereby bypassing the need to worry about real valued time, which wouldn't work with TLC anyway). This specific example is to turn the lights on and off, but in any case no less than every K seconds. However, it does not model check (invariant TimingOK violated) although it *seems* correct to me. The problem is that there is no way of forcing the LNext action to take place so the invariant is violated. (for the example I used K=2 and MAX_TIME 4). Is there a way to fix this so TLC will model check it?

thanks!

(*turn lights on and off, but at least every K seconds*)

EXTENDS Naturals

CONSTANTS

MAX_TIME, K

Time == 0 .. (MAX_TIME+1) 

VARIABLE lights,clock, lightsTrigT

vars == <<lights, clock, lightsTrigT>>

isTyped == lights \in BOOLEAN /\ clock \in Time /\ lightsTrigT \in Time

Init == lights=TRUE /\ clock=0 /\ lightsTrigT=0

LNext == (IF lights THEN lights'=FALSE ELSE lights'=TRUE) /\ lightsTrigT' = clock

DoNothing == UNCHANGED <<lights,lightsTrigT>>

clockNext == clock' = clock+1 

TBound(actionTriggerT, maxWait) == clock <= actionTriggerT + maxWait

Next == (LNext \/ DoNothing) /\ clockNext /\ TBound(lightsTrigT, K)

Spec == Init /\ [][Next]_vars

TimingOK == (clock <= lightsTrigT + K)

THEOREM Spec => [] TimingOK

[ns]

Sorry a correction: the TBound is clock < actionTriggerT + maxWait. The problem is deadlock not invariant not being satisfied.

[Stephan Merz]

Not sure I understand your question: TLC *does* model check your spec, it just (correctly) signals a deadlock, since the non-clock variables may stutter according to DoNothing until the clock exceeds its bound, at which point no action is enabled anymore. If you intend to avoid this, DoNothing needs a stronger time bound, see attached module for a possible definition.

Since the modified spec generates an unbounded state space, you'll need to add a state constraint to your model, such as 

clock <= MAX_TIME

Hope this helps,

Stephan

[ns]

hi Stephan, thanks as always for your insightful answer. My thinking was that since the spec doesn't admit any traces in which the lights don't change at least once every K s (based on my understanding of TLA semantics) I was hoping that the model checker would agree and say that the invariant was indeed satisfied. But instead it reported deadlock. I did see where the deadlock is coming from,  and I suppose its a way of rejecting those bad traces, but was somewhat surprising. I like your solution to the problem using a kind of "lookahead" to prevent DoNothing when a bound is about to expire, but it appears to me a way of getting TLC to do the right thing. Please let me know if I'm still missing something key.

[ns]

But perhaps one answer here is that while the spec doesn't admit any traces in which the invariant is violated, it does admit finite traces (ie those that deadlock) and that is what TLC is catching. However, given TLA semantics, only infinite traces can be traces of the model so finite traces don't or shouldn't enter the picture.

[Stephan Merz]

First, you can of course ignore the deadlock by disabling deadlock checking if you are not interested in it.

Second, a state is deadlocked if `ENABLED Next' is false at that state, but the actual transition relation is [Next]_vars, so a finite behavior ending in a deadlocked state can always be extended to an infinite behavior.

Stephan

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[Earnshaw]

Hi ns, this is my spec  to solve the problem, hope it can help:

-------------------------------- MODULE Time --------------------------------

(*turn lights on and off, but at least every K seconds*)
EXTENDS Naturals
CONSTANTS
MAX_TIME, K

Time == 0 .. MAX_TIME

VARIABLE lights,clock, lightsTrigT
vars == <<lights, clock, lightsTrigT>>

isTyped == lights \in BOOLEAN /\ clock \in Time /\ lightsTrigT \in Time

Init == lights=TRUE /\ clock=0 /\ lightsTrigT=0

\*Init == lights=FALSE /\ clock=10 /\ lightsTrigT=10

TBound(actionTriggerT, maxWait) == clock < actionTriggerT + maxWait
                 
clockNext ==  /\ TBound(lightsTrigT, K)
              /\ IF TBound(lightsTrigT, K-1)
                 THEN
                  /\ clock' = clock+1
                  /\ UNCHANGED <<lights,lightsTrigT>>
                 ELSE \*clock = (lightsTrigT + K -1)
                  /\ (IF lights THEN lights'=FALSE ELSE lights'=TRUE)
                  /\ clock' = clock+1
                  /\ lightsTrigT' = clock'
                                                                                   
Next == clockNext

Spec == Init /\ [][Next]_vars

TimingOK == clock <= lightsTrigT + K
           
Test == clock # 10

THEOREM Spec => [] TimingOK

=============================================================================