Homework 3

[Note: this webpage last modified Tuesday, 15-Feb-2011 14:43:51 EST]

This homework assignment is due before class starts on Tuesday, February 15. Your solutions should be explained in complete sentences such that your classmates will understand the solution (and can verify your proofs are correct) even if they have not solved the problems themselves.

  1. HW Polices.

    1. Type your HW (in word, latex, text file, etc.) and send to me by email.

    2. Do NOT share electronically. You must type your own solutions. You can discuss the problems with each other, but you may only discuss them. You may not write out solutions together.

    3. You MAY NOT search the Internet, textbooks, etc. for solutions to the problems. The following are the ONLY sources of information that you may use in solving the problems: the textbook for this course, wikipedia articles on basic math/probability/etc., and mathematical review material at the following MIT opencourseware page: 6.042J / 18.062J Mathematics for Computer Science, Fall 2005. You may discuss the problems with each other and with myself, but must obey the previous item in doing so.

      If you do find the solution in one of these three sources, you still MUST cite the source in your document.

      You may use NOTHING ELSE that is online or other textbooks.

    4. You MAY NOT copy word-for-word from any source, even the three you are allowed to consult. If you feel it is necessary, you should put the quotation in quotes and provide a reference/citation.

  2. (-2 points if left blank) List who you collaborated with on this assignment, "none" if none.

  3. (10 Points) Originally assigned on hw2, now part of hw3. Find a problem that is not decidable which we have not covered in class and is not given in the book. Give a proof that the problem is not decidable that takes less than one page. You may consult any source for this problem, but you may not copy word for word, and you must cite the source. When you are typing your solution, you should not have your source in front of you. You can reserve a problem by emailing me. You will present your solution for this problem or the next problem after the assignment is turned in.

    Problems chosen: totality problem (Prudhvi), Post correspondence (Subu, see Sipser textbook Introduction to the Theory of Computation for proof), equivalence (Nihar), membership (Kranthi), tiling (Masood, proof), totality problem (Chandana, proof), emptiness (Sujana),

  4. (Extra Credit, 2 Points) For the NP-complete problem you chose, write a program to solve the problem by brute force. For example, to solve the SAT problem by brute force, you would take as input a Boolean formula and then try all possible assignments to the variables. You can write the program in whatever programming language you choose, but it must compile and work properly. You should attach the file as a separate attachment to your homework.