Exercise 1: (a) One technique to show that a decision problem is undecidable is to reduce a known...1 answer below »

Exercise 1:

(a) One technique to show that a decision problem is undecidable
is to reduce a known undecidable problem, like the Halting Problem,
to the problem of concern. Explain what requirement on that
reduction (besides being a reduction, of course) is fundamental for
this approach to work. Also, state which Theorem in Sudkamp's book
makes use of this requirement.

(b) Prove that the problem of deciding whether a Turing Machine
M and a DFA D are such that L(M) = L(D) is undecidable.

(c) Consider the following two decision problems:

P1: Given a Turing machine T and a string w, are there more than
one way (i.e., more than one execution) the machine T can accept
w

P2: Given a Turing machine T and a string w, does T accept
w?

Use the fact that problem P2, has already been shown undecidable
, to prove that problem P1, is also undecidable.

Exercise 1: Undecidability 35 marks la) 5 marks) One technique to show a decision problemisundecidable is lo roduee a known undecida ble problem, like the Halting Problem.lothe problemofconcern, Explain what requirement onthatreduction (besides being a reduction, of course fasadamental for approach to work. Aba, stale which Theorem n Sudkamp's book makes u of this requirement (b) [15 marks) Prove that the problem of deciding whether a Turing Machine Mand a DEA Dare suc Ih L(D) is undecidable. c) (15 marks) Consider the following two decision problems Pi: Given a Turing machine Tand a string are there more than one way (ie. more than one execution he machine T can acce F Given a Turing machine T and a string does Taccept er? Use the fact that probe Pi has already been shown undecidable (in the tutorial ).to prove that problem F1 is also undecidable.

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