Restrictions for loop-check in sequent calculus for temporal logic

In this paper, we present sequent calculus for linear temporal logic. This sequent calculus uses efficient loop-check technique. We prove that we can use not all but only several special sequents from the derivation tree for the loop-check. We use indexes to discover these special sequents in the sequent calculus. These restrictions let us to get efficient decision procedure based on introduced sequent calculus.