We study the computational complexity of finding a line that bisects simultaneously two sets in the two-dimensional plane, called the pancake problem, using the oracle Turing machine model of Ko. We also study the basic problem of bisecting a set at a given direction. Our main results are: (1) The complexity of bisecting a nice (thick) polynomial-time approximable set at a given direction can be characterized by the counting class #P. (2) The complexity of bisecting simultaneously two linearly separable nice (...) (thick) polynomial-time approximable sets can be characterized by the counting class #P. (3) For either of these two problems, without the thickness condition and the linear separability condition (for the two-set case), it is arbitrarily hard to compute the bisector, even if it is unique. (shrink)
Editor's Note: Over a long period of time, the evil bourgeois reactionary line has created antagonism between two groups of students in schools—antagonism on the basis of one's family background. This antagonism became very obvious during the initial stage of the Cultural Revolution, and has lasted to this day. It has prevented further criticism of the bourgeois reactionary line and hindered further development of the Cultural Revolution.
The Rising Sun Battlefield Journal published by the East-Is-Red Commune of the Beijing Institute of Light Industry devoted as many as six pages to an all-out attack of "On Family Background" in a long and despicable article titled "The Big Poisonous Weed ‘On Family Background’ Must Be Torn Up by the Roots." In their own words, the appearance of this article was inevitable at a time when the Cultural Revolution reached the stage of great alliance [of mass rebel organizations] and (...) the great power seizure [from capitalist-roaders within the Party]. (shrink)
In December of last year, a few clowns appeared on the grand and spectacular stage of the Great Proletarian Cultural Revolution. These clowns were the reincarnated ghosts from the Capital Red Guard West City, East City, and Haidian Districts Pickets. They viciously attacked Chairman Mao's revolutionary line, engaged in slander on the Central Cultural Revolution Group, called dear Comrade Jiang Qing names, and sabotaged the organizations under the proletarian dictatorship. They provoked violence, created chaos, searched and confiscated the possessions of (...) revolutionary organizations, and spread reactionary declarations. The crimes they committed are simply too numerous to mention. These clowns were none other than the "Capital Red Guards United Action Committee.". (shrink)