0

I'm studying Turing Machines and I've already showed how Turing-Decidable is closed for the operations of Union, Intersection, Concatenation, Complement and Kleene Star. Next I did some demonstrations to show how T-Recognizable languages are closed for Union, Intersection, Concatenation and Kleene Star.

Now I'm trying to answer a question to show why the classe of T-Recognizable languages are not closed for the operation of Complementation, but I cannot understand it. Could someone please explain this?

Thanks

Blacklight Shining
  • 1,468
  • 2
  • 11
  • 28
Sasha Fonseca
  • 2,257
  • 23
  • 41

1 Answers1

2

  1. T-recog corresponds to semi-decidable (r.e.).

  2. Convince yourself that a language is exaclty then decidable, when both, the language itself and its relative complement are r.e.

  3. Convince yourself that there are r.e. languages that are not decidable (e.g. Halteproblem)

  4. Assume that the class of r.e. languages is closed under complementation and derive a contradiction to the facts mentioned in 2. and 3.

D.F.F
  • 914
  • 1
  • 6
  • 17