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LTL satisfiability problem

0 votes

Exam Problem : 13.02.2019 Q 8 (b) : 2019.02.13.vrs.solutions.pdf (uni-kl.de)

This satisfies S1 and not S2.

As per my intuition, in s1 a is true and until that Fb is false, which makes S2 unsatisfied but I am confused for S1 as a is true in s3 but b is true in only s2 and not s0 and s1.

So here how could I interpret F [b SU a], does the below solution makes sense in this case ?

Could you please explain about this ?

in * TF "Emb. Sys. and Rob." by (2.9k points)

1 Answer

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The first Kripke structure satisfies both S1 and S2:

                   0 1 2 3 3 ...
        [b SU a] : 0 1 1 1 1 ...
       F[b SU a] : 1 1 1 1 1 ...
              Fb : 1 1 1 0 0 ...
       [Fb SU a] : 1 1 1 1 1 ...

For the second structure, we have the following

                   0 1 2 2 ...
        [b SU a] : 0 1 1 1 ...
       F[b SU a] : 1 1 1 1 ...
              Fb : 1 1 1 1 ...
       [Fb SU a] : 1 1 1 1 ...
by (170k points)

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