PROBLEM SOLVING 2 CS+X 3 CS+X SCULPTURE GEOLOGY FINANCE - PowerPoint PPT Presentation

CS+X 2017 AARON STOCKDILL PROBLEM SOLVING

2 CS+X

3 CS+X SCULPTURE GEOLOGY FINANCE MATHEMATICS COMPUTER SCIENCE

4 CS+X Problem Computer Mathematics Solving Science

5 CS+X What does it mean to solve a problem? Exploring languages with compression Problems we can't solve

6 WHAT DOES IT MEAN TO SOLVE A PROBLEM?

7 CS+X WHAT IS COMPUTER SCIENCE? Computer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. From Wikipedia, the free encyclopedia Computer science is as much about computers as astronomy is about telescopes. Edsger Dijkstra, supposedly…

8 CS+X WHAT IS A COMPUTER?

9 CS+X WHAT IS A COMPUTER? λ f. ( λ x. ( f ( x x )) λ x. ( f ( x x ))) Turing Machine Lambda ( λ ) Calculus

10 CS+X CHURCH-TURING THESIS “A problem can be solved by an algorithm iff it can be solved by a Turing Machine ” Lambda Calculus Magic: The Gathering Music notation

11 CS+X ALGORITHM ≡ FORMAL SEQUENCE OF STEPS was_boring = False while speaker.is_speaking(): self.listen() if speaker.is_boring(): self.boo() was_boring = True if not was_boring: self.cheer()

12 EXPLORING LANGUAGES WITH COMPRESSION

13 CS+X LANGUAGES CAN BE SIMILAR Olá, estou bem Portuguese Hola, estoy bien Spanish Hallo, mir geht es gut German

14 CS+X WHAT DOES “SIMILAR” MEAN? NCD Z ( x, y ) = Z ( xy ) − min { Z ( x ) , Z ( y ) } max { Z ( x ) , Z ( y ) } “How similarly do two different things compress?”

15 CS+X UNIVERSAL DECLARATION OF HUMAN RIGHTS

16 CS+X GENERAL CATEGORISATION ALGORITHM Genomes / Phylogenetics Plagiarism Music Genres Determining File Types

17 PROBLEMS WE CAN'T SOLVE

18 CS+X COMPLEXITY P = NP ?

19 CS+X COMPLEXITY P NP MST all vertices MST some searching Super Mario vertices sorting primality timetabling bin packing point-to-point gcd 3-SAT travelling shortest path salesman 2-SAT

20 CS+X COMPLEXITY P NP MST all vertices MST some searching Super Mario vertices sorting primality timetabling bin packing point-to-point gcd 3-SAT travelling shortest path salesman 2-SAT

21 CS+X UNCOMPUTABLE FUNCTIONS The Halting Problem Kolmogorov Complexity Busy Beaver Chaitin’s Constant

CS+X 2017 AARON STOCKDILL PROBLEM SOLVING