Exam 12: Models of Computation

List three practical consequences arising from unsolvable programs related to the halting problem.

The ____ states that if there exists an algorithm to do a symbol manipulation task, then there exists a Turing machine to do that task.

Models can only give us information about existing phenomena.

The bit inverter Turing machine should have two states. _________________________

What do we require any computing agent to be able to do?

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

A Turing machine includes a(n) tape that extends infinitely in both directions. _________________________

Explain how a Turing machine differs in scale from any real computing agent.

The ____ thesis can never be proved because the definition of an algorithm is descriptive, not mathematical.

Turing machines define the limits of ____, which is what can be done by symbol manipulation algorithms.

At any point in time, only a finite number of cells in the Turing machine input contain ____ symbols.

A(n) ____ is a visual representation of a Turing machine algorithm.

The Turing machine contains two separate units, one for input and one for output.

Discuss the ways in which a Turing machine does or does not satisfy the requirement that an algorithm be a well-ordered collection.

Each time a Turing machine operation is done, four actions take place. _________________________

We can write a Turing machine to add 1 to any number; such a machine is often called a(n) ____.

A formal basis for mathematical proofs guarantees the presence of intuitive statements.

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

What are four characteristics of the model of a physical or social phenomenon?

A formal basis for proofs might allow for ____ theorem-proving.