GATE (Graduate Aptitude Test in Engineering) Computer Science & IT (CS) Theory of Computation-Regular Languages and Finite Automata Study Material (Page 1 of 8)

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Computability

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Computability

Let us first go through the basic meaning of the term “computability” . To begin with, we will start with the mathematical connotation of the term. After covering the concept of “computability” , we will get a clearer view of what exactly Theory of Computation is supposed to mean in the Computer science realm.

  • In basic terms, performing a computation sounds like a simple enough task and it is easy to suppose that everything is computable. In fact, there are a range of different types of non-computability that we need…

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Computability: David Hilbert

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David Hilbert

  • As mentioned before, part of the impetus for the drive to codify what is computable came from the mathematician David Hilbert. Hilbert believed that all of mathematics could be precisely axiomatized. He felt that once this was done, there would be an “effective procedure” , that is an algorithm that would take as input any precise mathematical statement and after a finite number of steps, decide whether the statement was true or false. Hilbert was asking for a decision procedure for all of mathematics.
  • The computational depiction of the 8-state Turing machine, which we will cover later
  • As one would expect, the central id…

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