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Chapter 0: Q3E (page 1)

Show that if A鈮�TBand B鈮�TC, thenA鈮�TC .

Short Answer

Expert verified

Let us assume that M1Bdecides A and decides B.

We will use an oracle Turing MachineM3 such thatM3C decides A.

Let us makeM3 to simulate M1.

Now every time whenM1makes queries to its oracle about any string 鈥榵鈥�, our machineM2will check ifX鈭�Band give the output toM1.

This output is given toM1byM3becauseM3didn鈥檛 have oracle for B so can鈥檛 perform the check directly so it simulatesM2on input x to get details.

This makesA鈮�TB

Now, machineM3 is capable to obtain input from queriesM2 of as both of them use same oracle C.

This makes B鈮�TC.

Thus A鈮�TBand B鈮�TC, then A鈮�TC, that shows transitive relation on A,B and C on relation 鈥�鈮�T 鈥�.

Step by step solution

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Most popular questions from this chapter

Let 鈭�=0,1. Let B be the collection of strings that contain at least one 1 in their second half. In other words,

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