All the formulas of LTL can be transformed into negation normal form, where
- all negations appear only in front of the atomic propositions,
- only other logical operators true, false, ∧, and ∨ can appear, and
- only the temporal operators X, U, and R can appear.
Using the above equivalences for negation propagation, it is possible to derive the normal form. This normal form allows R, true, false, and ∧ to appear in the formula, which are not fundamental operators of LTL. Note that the transformation to the negation normal form does not blow up the size of the formula. This normal form is useful in translation from LTL to Büchi automaton.
Read more about this topic: Linear Temporal Logic
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