CS154 Spring 2013Practice Final

A practice exam will appear here a week before the actual exam.

To study for the final I would suggest you: (1) Know how to do (by heart) all the practice problems. (2) Go over your notes at least three times. Second and third time try to see how much you can remember from the first time. (3) Go over the homework problems. (4) Try to create your own problems similar to the ones I have given and solve them. (5) Skim the relevant sections from the book. (6) If you want to study in groups, at this point you are ready to quiz each other. The practice final is below. Here are some facts about the actual final: (a) It is comprehensive (b) It is closed book, closed notes. Nothing will be permitted on your desk except your pen (pencil) and test. (c) You should bring photo ID. (d) There will be more than one version of the test. Each version will be of comparable difficulty. (e) It is 10 problems, 6 problems will be on material since the midterm, four problems will come from the topics covered prior to the midterm. (f) Two problems will be exactly (less typos) off of the practice final, and one will be off of practice midterm

1. Briefly explain how a TM with tape alphabet `{0,1, \square}` can simulate a TM that has alphabet `{a,b,c,d, \square}`.
2. Define (a) `\mbox{TIME}(f(n))`, (b) what it means for an NTM to accept, (c) proper function (alternatively, time constructible).
3. Briefly explain how a RAM can be simulated by a TM.
4. Prove using a counting argument that some languages are not recursively enumerable.
5. Show the following complexity classes are not the same: DTIME(`n`) and NTIME(`n^3`). Show NP is contained in EXP.
6. Prove `A_(LBA)` is decidable. Show all necessary lemmas.
7. State the Post Correspondence Problem. Give an example of a set of dominos with a match, and an example set without.
8. Use Rice's theorem to show the set of encoding of TMs that recognize a language in PSPACE is undecidable.
9. Use the Recoursion Theorem to show `mbox(HALT)_{TM}` in undecidable.
10. Prove `exists c forall x[K(\x\x\x) leq K(x) + c]`.