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cal - give a counter-example 3 a Prove that any number n so...

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CSE 200 Computability and Complexity Calibration Homework Due April 7 March 29, 2010 1. Let Reg k be the class of languages accepted by a deterministic finite automaton with at most k states. Prove that for every k > 0, Reg k is a strict subset of Reg k +1 . 2. Let f be a non-decreasing, positive integer-valued function over the positive integers. Prove that if f (2 n ) O ( f ( n )), then there is a k so that f ( n ) O ( n k ). Is the coverse always true? Prove it or
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Unformatted text preview: give a counter-example. 3. a. Prove that any number n so that n mod 4 = 3 has a prime factor p with p mod 4 = 3. b. Prove that there are inFnitely many primes p with p mod 4 = 3. 4. In your favorite programming language, write a program that takes no input and prints itself (its own code). Your program may not make system calls. 1...
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