Monday, January 26

The Universe of Problems

We illustrated the universe of all (well-defined) problems by carving a diagram of this universe into known components. 

• Decision problems
  • decidable problems
  • undecidable but Turing recognizable
  • not Turing recognizable
  • tractable
  • intractable
• General problems
  • Turing computable problems (corresponding to problems that are represented by total recursive functions)
  • Turing computable problems (corresponding to problems that are represented by partial recursive functions)
  • Problems that have no Turing machine that even computes a partial recursive function
  • tractable problems
  • intractable problems

Why Decision Problems?

We discussed the reasons for focusing on decision problems when exploring both computability and complexity.