Assign4ans_2 - CS5371 Theory of Computation Homework 4(Suggested Solution 1 Ans Suppose on the contrary that T is decidable Let R be its decider

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CS5371 Theory of Computation Homework 4 (Suggested Solution) 1. Ans. Suppose on the contrary that T is decidable. Let R be its decider. Then, the following TM Q is a decider for A TM : Q = “On input h M,w i , 1. Construct a TM M 0 as follows: M 0 = “On input x , 1. If x 6 = 011 , accept . 2. Run M on w . 3. If M accepts w , accept .” 2. Run R to decide if h M 0 i is in T . 3. If yes (i.e., R accepts), accept . 4. Else, reject .” It is easy to check that Q runs in finite steps. Also, in Step 1, M 0 has the property that: (i) If M accepts w , L ( M 0 ) = Σ * , so that h M 0 i ∈ T . (ii) Else, L ( M 0 ) = Σ * - { 011 } , so that h M 0 i / T . So, if Q accepts h M,w i , it must mean that R accepts h M 0 i , which implies that h M 0 i ∈ T , which implies M accepts w . On the other hand, if Q rejects h M,w i , R rejects h M 0 i , which in turn implies that M does not accept w . Thus, Q is a decider for A TM , and a contradiction occurs. So, we conclude that T is undecidable. 2. In the
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/22/2010 for the course CS 881 taught by Professor H.f. during the Spring '10 term at Shahid Beheshti University.

Page1 / 2

Assign4ans_2 - CS5371 Theory of Computation Homework 4(Suggested Solution 1 Ans Suppose on the contrary that T is decidable Let R be its decider

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online