Lecture 7 - Computability Intro Flashcards
What is the model of a computer?
Something that takes an input , does something and produces an output.
What is that something (black box)?
a function that maps input to output
What is computability concerned with?
which functions can be computed
- what problems can be solved by a computer
Example of an unsolvable problem?
One that can’t be solved even with unbounded time e.g. tiling problem
What is the tiling problem?
a set of squares with 4 triangles of some colours
the squares cannot be rotated
can any finite area of any size be completely covered using only tiles in the set, so that the adjacent colours match
To form a 3x3 square, how many possibilities is there?
3^9
Is there an algorithm for the tiling problem?
No
Why is there a problem with the tiling problem?
As ‘any size’ means we have to check all finite areas and there is inifinitely many of those
For certain set of tiles there is no repeated pattern we can use
Correct algorithm would have to check all finite areas
What is an undecidable problem?
A decision problem that cannot be solved.
Another word for unsolvable?
non-computable
What is the PCP problem
Post’s correspondence problem
- two finite sequences of words
- does there exist a sequence of integers chosen such that the concatenate words form the same result
Example of pcp
x1 = aab x2 = a
y1 = bbab y2 = aa
2 1 1 …. gives the same sequence of aaab (with more - refer to slide 15)
Is pcp unsolvable or undecidable?
undecidable
