Created: Wed 02 Dec 2009
Wed 02 Dec 2009
Wed 09 Dec 2009
- Please review the
outlined in the course information page.
- On the first page of each part of your solution write-up,
you must make explicit which problems are to be graded for
"regular credit", which problems are to be graded for "extra credit",
and which problems you did not attempt.
Please use a table something like the following
where "RC" is "regular credit", "EC" is "extra credit", and "NA"
is "not applicable" (not attempted). Failure to do so will result
in an arbitrary set of problems being graded for regular
credit, no problems being graded for extra credit, and a five percent
- You must also write down with whom you worked on the assignment. If this
changes from problem to problem, then you should write down this
information separately with each problem.
- This assignment cannot be accepted late since
solutions for this assignment will be handed out the day that
it is due.
Required: 4 of the following 7 problems
Points: 25 pts per problem
- Problem 7.20 (b). Note: You have already shown that LPATH is in
NP (HW08); you need not repeat that portion of the proof.
- Problem 7.21. Hint: Reduce from SAT or 3SAT. You may do so by
adding one extra clause to the given formula.
- Problem 7.24
- Problem 7.28. Hint: Reduce from NOT-EQUAL-3SAT, defined in
Problem 7.24. (You need not solve Problem 7.24 to solve this
- Problem 7.26. Hint: Reduce from 3SAT. Each card will correspond
to a variable, and flipping the card will correspond to setting its truth
value. Each row on a card will correspond to a clause, and the absence or
presence of a hole will correspond to whether that clause is satisfied
by the variable setting or not. You will need one additional specially
designed card as well.
- Problem 7.34
- Problem 7.41. Hint: Your NFA will "guess" (via epsilon transitions)
the clause that will not be satisified and then verify that the clause
is not satisfied. There are c clauses, and to verify that any
clause is unsatisfied will require roughly m states, thus yielding
an O(cm) sized NFA. Finally, if the cnf-formula is unsatifiable,
what will be true about the language accepted by the NFA you construct?
What is the minimum equivalent such NFA? How could you use this to solve
SAT? See also Problem 6 from HW07.