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# Moncler Jackets Outlet Uk formulas where logical implication → is

We consider Boolean formulas where logical implication (→) is the only operator and all variables, except at most one (denoted

*Discount Moncler Jackets Women*z), occur at most twice. We show that the problem of determining falsifiability for formulas of this class is NP-complete but if the number of occurrences of z is restricted to be at most k then there is an O(|F|k) algorithm for certifying falsifiability. We show this hierarchy of formulas, indexed on k, is interesting because even lower levels (e.g., k=2) are not subsumed by several well-known polynomial time solvable classes of formulas. Let v be a cooperative (TU) game and v = v1 − v2 be a decomposition of v as a difference of two convex games v1 and v2. Then the core C(v) of the game v has a similar decomposition C(v) = C(v1) ⊖ C(v2),__Moncler Jackets Outlet Uk__where ⊖ denotes the Minkowski difference. We prove such a decomposition as a consequence of two claims: the core of a game is equal to the superdifferential of its continuation, known as the Choquet integral, and the superdifferential of a difference of two concave functions equals the Minkowski difference of corresponding superdifferentials.