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5.2 Turing Machines

Explore the early development of theoretical computer science with a focus on Turing machines and the influential work of Alan Turing. Learn about how Turing formalized the concepts of algorithm and computation, and how certain functions cannot be computed independently of memory and runtime.

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Questions and Answers

What did Alan Turing formalize in the early development of theoretical computer science?

Concepts of algorithm and computation

In which year was the paper 'On Computable Numbers, with an Application to the Entscheidungsproblem' submitted by Alan Turing?

1936

What question introduced by David Hilbert was related to the 'Entscheidungsproblem'?

Question of decision problem

What concept did Gödel's incompleteness theorems demonstrate before Alan Turing's work?

<p>Theorems that lack proofs</p> Signup and view all the answers

What question concerned the existence of an algorithm to determine whether mathematical theorems are true or false?

<p>'Entscheidungsproblem'</p> Signup and view all the answers

Where did Alan Turing study and devote much time to studying computability?

<p>Cambridge University</p> Signup and view all the answers

What role does a natural number play in the context of a Turing machine?

<p>It encodes a Turing machine as a program.</p> Signup and view all the answers

What distinguishes a non-deterministic Turing machine from a deterministic one?

<p>It has multiple instructions for each state and input symbols combination.</p> Signup and view all the answers

How is non-determinism relevant in complexity theory despite its rare practical relevance?

<p>It plays a crucial role in understanding computational complexity.</p> Signup and view all the answers

How do non-deterministic Turing machines handle multiple possible instructions for the same state and input symbols?

<p>They execute all possible instructions simultaneously.</p> Signup and view all the answers

In the context of non-deterministic Turing machines, what role does guessing play in the computation?

<p>It helps in avoiding non-accepted paths.</p> Signup and view all the answers

How does non-determinism influence the behavior of concurrent processes accessing shared data?

<p>It introduces ambiguity depending on the order of data access.</p> Signup and view all the answers

What was the name of the advanced cryptographic machine used by the Germans during the Second World War?

<p>Enigma</p> Signup and view all the answers

Which computer, based on electronic tubes, was developed by Turing to support decryption efforts during the war?

<p>Colossus</p> Signup and view all the answers

What computer did Turing work on programming after the war which studied questions related to artificial intelligence?

<p>Manchester Mark I</p> Signup and view all the answers

What significant test did Turing develop to evaluate a machine's ability to exhibit intelligent behavior equivalent to a human?

<p>Turing Test</p> Signup and view all the answers

What did Turing develop that is used to assess whether a machine can exhibit behavior indistinguishable from that of a human?

<p>Turing Test</p> Signup and view all the answers

What led to Turing's conviction in 1952 and subsequent depression?

<p>Hormone therapy</p> Signup and view all the answers

In which year did Turing die, most likely by suicide?

<p>1954</p> Signup and view all the answers

Which machine is described as consisting of a storage tape, individual cells, and a read/write head?

<p>Turing Machine</p> Signup and view all the answers

What is one of the elements of a program for a Turing machine as described in the text?

<p>z0 being the end state</p> Signup and view all the answers

How is an instruction z, b z', b', v for a Turing machine interpreted?

<p>Transition into next machine state</p> Signup and view all the answers

What is the Turing machine initially reading in?

<p>a</p> Signup and view all the answers

What is the tape content after the first computation step?

<p>ab</p> Signup and view all the answers

Which symbol denotes an empty cell in the tape?

<p>_</p> Signup and view all the answers

What does the tape content 'bb' represent in terms of the Turing machine state?

<p>State z1</p> Signup and view all the answers

Which part of the tape content represents what is behind the cell just read?

<p>Third part</p> Signup and view all the answers

What is a Turing-computable function?

<p>A function that can be computed with a universal Turing machine</p> Signup and view all the answers

What is the purpose of a universal Turing machine?

<p>To simulate every other Turing machine</p> Signup and view all the answers

'Gödelization' is a procedure used by Turing for what purpose?

<p>For proving incompleteness theorems for predicate logic</p> Signup and view all the answers

What limitation was overcome by introducing Universal Turing Machines?

<p>Limitation of running only one type of program</p> Signup and view all the answers

What happens when a Turing machine reaches the end state?

<p>It accepts the input word regardless of tape contents</p> Signup and view all the answers

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