prove formally that if the DDH problem is hard, then also is the CDH problem. Prove formally that if the CDH problem is hard then so is the dolog problem.
prove formally that if the DDH problem is hard, then also is the CDH problem. Prove...
Is the exclusive disjunction (operator ) of two equivalence
relations also an equivalence relation? Prove your conclusion
formally.
Subject Is the exclusive disjunction (operator ) of two equivalence relations also an equivalence relation? Prove your conclusion formally.
Prove formally that L3 is Turing-recognizable, where L3 = {(M, A) | TM M and DFA A accept a string in common.}
1. [4 pts) Formally prove (i.e. using € - 8 definition) that the function x3 is uniformly continuous on the interval (1,5).
Formally prove the following four statements (i.e., show a constant c and a no such that ): I. 2n is Θ(2n+1) 2. 3 is O(1) 3. 3n2 +4-2n is O(n3) 4. Σί-01 is Ω(n)
4. You do not need to formally prove your answers to the following (a) Find the inverse of the cycle σ (al a2 am) .. Exp ress vour answer in cyclic notation (b) Find the order of a cycle ơ-a1 a2 . . . amje Sn. (c) Find a formula for the order of any permutation σ E Sn based on its disjoint cycle decomposition
4. Prove that the sup norm on Rn is actually a погm. Hint: The hard part is the triangle inequality. Notice that the sup norm on R is just distance in R which by problem 1 must satisfy the triangle inequality
Why is the Jacobian Conjecture so hard to prove when only a little knowledge beyond Calculus is needed to understand it?
Algorithm problem 5 [3.2-3] Prove equation (3.19). Also prove that n!∈ω(2n) and n!∈o(n^n).
Problem 3 (10 points) Prove that a two-input multiplexor is also universal by showing how to build the NOR gate using multiplexors.
Problem 3 (10 points) Prove that a two-input multiplexor is also universal by showing how to build the NOR gate using multiplexors