Misconceptions In FiniteTrace and InfiniteTrace Linear Temporal Logic
Posted on 07 July 2024.Over the past three years and with a multinational group of collaborators, we have been digging deeper into misconceptions in LTL (Linear Temporal Logic) and studying misconceptions in LTLf, a promising variant of LTL restricted to finite traces. Why LTL and LTLf? Because beyond their traditional uses in verification and now robot synthesis, they support even more applications, from image processing to webpage testing to processrule mining. Why study misconceptions? Because ultimately, human users need to fully understand what a formula says before they can safely apply synthesis tools and the like.
Our original post on LTL misconceptions gives more background and motivation. It also explains the main types of questions we use: translations between English specifications and formal specifications.
So what’s new this time around?
First, we provide two test instruments that have been field tested with several audiences:

One instrument [PDF] focuses on the delta between LTL and LTLf. If you know LTL but not LTLf, give it a try! You’ll come away with handson experience of the special constraints that finite traces bring.

The other instrument [PDF] is for LTL beginners — to see what preconceptions they bring to the table. It assumes basic awareness of G (“always”), F (“eventually”), and X (“next state”). It does not test the U (“until”) operator. Live survey here.
Second, we find evidence for several concrete misconceptions in the data. Some misconceptions were identified in prior work and are confirmed here. Others are new to this work.
For example, consider the LTLf formula:
G(red => X(X(red)))
. What finite traces satisfy it?In particular, can any finite traces that have
red
true at some point satisfy the formula?Click to show answer:
No, because wheneverred
is true it must be true again two states later, but every finite trace will eventually run out of states.
Now consider the LTL formula
F(X(X(red)))
. Is it true for an infinite trace wherered
is true exactly once?Click to show answer:
Yes. But interestingly, some of our LTL beginners said no on the grounds thatX(X(red))
ought to "spread out" and constrain three states in a row.
Third, we provide a code book of misconceptions and how to identify them in new data [PDF].
For more details, see the paper.
See also our LTL Tutor (traditional LTL only, not finitetrace).