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Big O Notatation

Big O Notatation. How long will it take? How much memory will it use? Order of Magnitude Notation instance size n f(n) <= c g(n) for all n >= N than, f(n) = O(g(n)) O(n) < O(n log n)<O(n 1/2 )<O(n 2 )<O(2 n ). Satisfiability (SAT). Boolean Expression:

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Big O Notatation

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  1. Big O Notatation • How long will it take? • How much memory will it use? • Order of Magnitude Notation • instance size n • f(n) <= c g(n) for all n >= N • than, f(n) = O(g(n)) • O(n) < O(n log n)<O(n1/2)<O(n2)<O(2n)

  2. Satisfiability (SAT) • Boolean Expression: • (x1+~x3+x4)(~x1+~x2+~x4)(~x2+x3)(~x1+x2+x4) • What combination of variable values (0,1) makes statement true or false (1,0) • 2n combinations • Decision problem: Is formula satisfiable?

  3. NP-complete • NP: Nondeterministic Polynomial Time • 1970, Cook found way to transform every problem in NP to a single, complete problem (satisfiability). • Transform in polynomial time • Instance of one problem has solution if and only if instance of other problem does • Solve any instance of any problem equivalent to solving some instance of SAT

  4. Cellular Automata • An automaton. A copy on each cell in n-dimensional grid • A neighborhood function that specifies which of the cell’s adjacent cells affect its state. • A transition function that specifies mapping from state of neighbor cells to state of given cell

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