 An alternative view emphasizes the non-Boolean structure of properties of quantum systems. The properties of a classical system form a Boolean algebra, essentially the abstract characterization of a set-theoretic structure. This is reflected in the Boolean character of classical logic, and the Boolean gates in a classical computer. From this perspective, the picture is entirely different. Rather than ‘computing all values of a function at once,’ a quantum algorithm achieves an exponential speed-up over a classical algorithm by computing the answer to a disjunctive or global question about a function (e.g., whether a Boolean function is constant or balanced) without computing redundant information (e.g., the output values for different inputs to the function). A crucial difference between quantum and classical information is the possibility of selecting an exclusive disjunction, representing a global property of a function, among alternative possible disjunctions — for example, the ‘constant’ disjunction asserting that the value of the function (for both arguments) is 0 or 1, or the ‘balanced’ disjunction asserting that the value of the function (for both arguments) is the same as the argument or different from the argument — without determining the truth values of the disjuncts.