4. After graduating from the University of Michigan, you have decided to teach a computer science...
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4. After graduating from the University of Michigan, you have decided to teach a computer science course of your own. You create for your students some projects to complete, and now you want to write a program that will allow you to efficiently check if a student's code wrong in any way. In order to ensure your efforts are not wasted, you decide to use your 376 knowledge and construct a proof that this is possible. You come up with the following language and proof: LAUTOGRADER = {(Prog.cpp) : Prog.cpp is a C++ program that fails at least one test case out of T = t₁, t2,. , tn 2} ..." What is wrong with the following (faulty) "proof" that LAUTOGRADER E NP? "Proof". Define verifier V((Prog.cpp), (ti, k)): (a) Verify that t; is a test case in T. (b) Run Prog.cpp on test case ti for up to k steps. (c) If Prog.cpp returns false (i.e. it fails) within these k steps, accept; otherwise, reject. If (Prog.cpp) LAUTOGRADER, then Prog.cpp must fail on some test case t; after some finite number of steps k, which means that V((Prog.cpp), (ti, k)) will accept. And if (Prog.cpp) #LAUTOGRADER, then V will reject no matter what certificate (tį, k) is provided. Therefore, V is an efficient verifier for LAUTOGRADER, SO LAUTOGRADER E NP. 4. After graduating from the University of Michigan, you have decided to teach a computer science course of your own. You create for your students some projects to complete, and now you want to write a program that will allow you to efficiently check if a student's code wrong in any way. In order to ensure your efforts are not wasted, you decide to use your 376 knowledge and construct a proof that this is possible. You come up with the following language and proof: LAUTOGRADER = {(Prog.cpp) : Prog.cpp is a C++ program that fails at least one test case out of T = t₁, t2,. , tn 2} ..." What is wrong with the following (faulty) "proof" that LAUTOGRADER E NP? "Proof". Define verifier V((Prog.cpp), (ti, k)): (a) Verify that t; is a test case in T. (b) Run Prog.cpp on test case ti for up to k steps. (c) If Prog.cpp returns false (i.e. it fails) within these k steps, accept; otherwise, reject. If (Prog.cpp) LAUTOGRADER, then Prog.cpp must fail on some test case t; after some finite number of steps k, which means that V((Prog.cpp), (ti, k)) will accept. And if (Prog.cpp) #LAUTOGRADER, then V will reject no matter what certificate (tį, k) is provided. Therefore, V is an efficient verifier for LAUTOGRADER, SO LAUTOGRADER E NP.
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The proof provided is incorrect because it does not satisfy the definition of a verifier for the lan... View the full answer
Related Book For
Project Management The Managerial Process
ISBN: 9781260570434
8th Edition
Authors: Eric W Larson, Clifford F. Gray
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