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
Famous quotes containing the words negation, normal and/or form:
“Michelangelo said to Pope Julius II, “Self negation is noble, self-culture is beneficent, self-possession is manly, but to the truly great and inspiring soul they are poor and tame compared to self-abuse.” Mr. Brown, here, in one of his latest and most graceful poems refers to it in an eloquent line which is destined to live to the end of time—”None know it but to love it, None name it but to praise.””
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“To try to control a nine-month-old’s clinginess by forcing him away is a mistake, because it counteracts a normal part of the child’s development. To think that the child is clinging to you because he is spoiled is nonsense. Clinginess is not a discipline issue, at least not in the sense of correcting a wrongdoing.”
—Lawrence Balter (20th century)
“It may be said that the elegant Swann’s simplicity was but another, more refined form of vanity and that, like other Israelites, my parents’ old friend could present, one by one, the succession of states through which had passed his race, from the most naive snobbishness to the worst coarseness to the finest politeness.”
—Marcel Proust (1871–1922)