Editing Computability Theory (section)

== <span style="color: #FFFFFF;">Analyzing</span> ==
{| class="wikitable"
|+ Computable vs. Non-Computable
! Feature !! Computable (Sorting a list) !! Non-Computable (Shortest program)
|-
| Logic || Follows a finite set of steps || Requires 'Infinite' knowledge or luck
|-
| Outcome || Guaranteed answer || No algorithm exists
|-
| Machine || Standard computer (Turing Machine) || Requires an 'Oracle'
|-
| Analogy || Following a recipe || Deciding if a poem is 'Perfect'
|}

'''The Concept of "Reduction"''': This is how computer scientists solve problems. If you have a new problem, you try to "Reduce" it to an old one. "If I can solve X, I can solve Y." If we can reduce the Halting Problem to your problem, then your problem is also unsolvable. Analyzing these "Chains of Difficulty" is the core of computability theory.
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