Prove that a non-negative linear combination of a set of submodular functions is also a submodular function.
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Prove that a non-negative linear combination of a set of submodular functions is also a submodular function.
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- construct a programming-based version of the factorial function, and prove the time compexity.Prove that if the function f is 1-1, then f-1 is a function. 2.3 : Prove that the sum of the three variables of the sum exponent f(x) = Σe is strictly convex. For this i=1 purpose, compute the Hessian matrix of the function f(x).
- Using the three-variable Karnaugh-map below Solve for its corresponding function expression Replot the function from part (1) on a different three-variable Karnaugh-map (Hint: try a different combination of variables)Karnaugh maps and standard forms.For the following function:? (?, ?, ?, ?) = Σ? (0,1,2,5,8,9,10)1-) Write the minimal function in product-of-sums formNelson-Oppen Use the Nelson-Oppen procedure to prove that the following formula over the theories of uninterpreted functions and linear real-valued arithmetic is unsatisfiable: g(f(x – 2)) = x + 2 A g(f(y)) = y – 2A (y +1= x – 1)