Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In linear time logic, is $\mathbf{GF}p$ equivalent to $ \mathbf{G}p$ ?

$\mathbf{GF}p$ means that it is always the case that p is true eventually.

Let $\mathbf{G} p$ be defined as: $\forall j \ge0,\ p$ holds in the suffix $q_j, q_{j+1}, q_{j+2},\ldots$

and since: formula $φ$ holds for state machine $M$ if $φ$ holds for all possible traces of $M$

Isn't $\mathbf{G}$ in $\mathbf{GF}p$ redundant then?

share|cite|improve this question
up vote 4 down vote accepted

No, not equivalent and not redundant.

Consider $p$ being true if and only if $j$ is even. $\mathbf{G}p$ is not true (obviously, since $p$ is false in every odd state), but $\mathbf{GF}p$ is always true.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.