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Within the class there were two versions of a given test; however, these two versions were just problem permutations of each other. The results above are all for the first of these two permutations. LO1 (Learning Outcome 1) -- Exhibit a simulation of one machine model with another. For instance, a Turing machine by a RAM. LO2 -- Give a minimal classification of the complexity of a computational problem as being in one of the class L, P, NP, coNP, some level of the polynomial hierarchy, PSPACE, E, EXPTIME, decidable, undecidable. LO3 -- Show the completeness of a complete problem for each of these classes. LO4 -- Know properties of the randomized classes RP, BPP. LO5 -- Know conditions under which various of these hierarchies might collapse. LO6 -- Explain at least one circuit lower bound technique such as Razborov's techniques for monotone circuits. LO7 -- Exhibit a relativized separation (oracle result) of complexity classes for standard classes such as P and NP. N/A -- Important material covered in the course but not directly related to a specific learning outcome. |