# Doubt regarding Temporal Logics

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Hi,

How does E [a SU a ] holds only in {s0,s5}? There is a path from s3 -> s5 so why it doesn't hold in s3?

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[ a SU a ] means that we need to see the right hand a eventually, and on the way, the left hand a needs to be satisfied in every step. As all states other than {s0, s5} do not satisfy a, they also fail satisfying [ a SU a ]. Thus only {s0, s5} satisfy [ a SU a ]
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okay so we wont see path here? e.g. s3 is also eventually reaching a and in SU if we have reached /si then it would be true. s3-s5-s0-s5-s0...
[a SU a] is equivalent to just a. Thus, it holds on every infinite path that starts with a state labeled with a. The path  s3-s5-s0-s5-s0... you mention starts with state s3 that is labeled with c, but not with a. So [a SU a] does not hold on that path.
s3 does not satisfy the left hand criterion. Also is does not satisfy the right hand criterion. Thus, no path starting from s3 could satisfy [ a SU a ].

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