hw9 - A L ={h M i M accepts some even-length string B L ={h...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
ECS 120: Introduction to the Theory of Computation Homework 9 Problem 1. In the movie The Matrix there is a TM called The Oracle which can solve problems that other TMs cannot (even some that the TM Neo couldn’t!), although, as she states herself, there are problems that are even beyond her reach. Here, we’ll try to understand why. Define Halting Oracles as regular TMs but with the added functionality of a “black box” which allows them to decide A TM = {h M,w i| w L ( M ) ,M is a TM } instanta- neously. Prove that the language O TM = {h O,w i| w L ( O ) ,O is a Halting Oracle } is not decidable by a Halting Oracle. Problem 2. Classify the following languages as decidable , acceptable (but not decid- able), co-acceptable (but not decidable), or neither acceptable nor co-acceptable. Prove all your answers, giving decision procedures or reductions.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A. L = {h M i : M accepts some even-length string } . B. L = {h M i : M accepts some palindrome } . C. L = {h M i : M never prints a “0” (regardless of the input) } . D. L = {h φ i : φ is a Boolean formula which has no satisfying assignment } . Problem 3. Suppose you are given a polynomial time algorithm which, on input of a Boolean formula φ , decides if φ is satisfiable. Describe an efficient procedure which finds a satisfying assignment for φ . Problem 4. Prove that if P = NP then ∀ A ∈ P \ {∅ , Σ * } , A is NP-complete. Problem 5. Prove that DOUBLE-SAT= {h φ i| φ has at least two satisfying assignments } is NP-complete. 1...
View Full Document

This note was uploaded on 04/29/2010 for the course ECS 222 taught by Professor Mr. during the Spring '10 term at UC Davis.

Ask a homework question - tutors are online