  In this paper, we consider the problem of translating LTL formulas to Buechi
automata. We first translate the given LTL formula into a special
disjuctive-normal form (DNF). The formula will be part of the state, and its
DNF normal form specifies the atomic properties that should hold immediately
(labels of the transitions) and the formula that should hold afterwards (the
corresponding successor state). Surprisingly, if the given formula is
Until-free or Release-free, the Buechi automaton can be obtained directly in
this manner. For a general formula, the construction is slightly involved: an
additional component will be needed for each formula that helps us to identify
the set of accepting states. Notably, our construction is an on-the-fly
construction, and the resulting Buechi automaton has in worst case 2^{2n+1}
states where n denotes the number of subformulas. Moreover, it has a better
bound 2^{n+1} when the formula is Until- (or Release-) free.
