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A formal basis for proofs allows for ____ theorem-proving.


A) unsolvable
B) mechanical
C) indisputable
D) observable

E) B) and D)
F) B) and C)

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Each Turing machine instruction describes an operation that is unambiguous, requiring no additional explanation, and any Turing machine is able to carry out the operation described.

A) True
B) False

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A Turing machine includes a tape that extends infinitely in both directions.

A) True
B) False

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A(n) ____ is a statement advanced for consideration and maintained by argument.


A) algorithm
B) contradiction
C) thesis
D) 5-tuple

E) A) and B)
F) A) and C)

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The ____ deals with deciding if a collection of Turing machine instructions will ever halt.


A) Turing problem
B) parity problem
C) halting problem
D) incomputable problem

E) A) and D)
F) A) and C)

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Although we can compare two Turing machine algorithms for the same task, we cannot really compare the efficiency of a Turing machine algorithm that will be run on a "real" computer.

A) True
B) False

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The real value of Turing machines as models of computability is in exposing problems that are uncomputable.

A) True
B) False

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Which of the following statements about the halting problem is correct?


A) it is a computable problem
B) no Turing machine exists to solve this problem
C) a Turing machine exists that solves the problem
D) if it cannot be done by a Turing machine, it is still computable

E) All of the above
F) C) and D)

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Unsolvable problems related to the halting problem have the following practical consequence:


A) a program can be written to decide whether any given program run on any given input will produce some specific output
B) a program can be written to decide whether any two programs are equivalent
C) a program can be written to decide whether any given program always stops eventually, no matter what the input
D) no program can be written to decide whether any given program run on any given input will ever produce some specific output

E) C) and D)
F) A) and D)

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An extra bit, called a(n) ____, can be attached to the end of a string of bits.


A) state diagram
B) odd parity bit
C) algorithm
D) sentinel

E) C) and D)
F) B) and D)

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