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PROBLEM SOLVING
CS+X 2017 AARON STOCKDILL
CS+X 2
PROBLEM SOLVING 2 CS+X 3 CS+X SCULPTURE GEOLOGY FINANCE - - PowerPoint PPT Presentation
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
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GEOLOGY SCULPTURE FINANCE MATHEMATICS COMPUTER SCIENCE
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Mathematics Computer Science Problem Solving
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What does it mean to solve a problem? Exploring languages with compression Problems we can't solve
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WHAT DOES IT MEAN TO SOLVE A PROBLEM?
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WHAT IS COMPUTER SCIENCE?
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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…
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WHAT IS A COMPUTER?
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WHAT IS A COMPUTER?
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Turing Machine Lambda (λ) Calculus
λf.(λx.(f(x x))λx.(f(x x)))
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CHURCH-TURING THESIS
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“A problem can be solved by an algorithm iff it can be solved by a Turing Machine” Lambda Calculus Magic: The Gathering Music notation
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ALGORITHM ≡ FORMAL SEQUENCE OF STEPS
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was_boring = False while speaker.is_speaking(): self.listen() if speaker.is_boring(): self.boo() was_boring = True if not was_boring: self.cheer()
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EXPLORING LANGUAGES WITH COMPRESSION
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LANGUAGES CAN BE SIMILAR
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Portuguese
Olá, estou bem
Spanish
Hola, estoy bien
German
Hallo, mir geht es gut
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WHAT DOES “SIMILAR” MEAN?
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NCDZ(x, y) = Z(xy) − min{Z(x), Z(y)} max{Z(x), Z(y)}
“How similarly do two different things compress?”
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UNIVERSAL DECLARATION OF HUMAN RIGHTS
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GENERAL CATEGORISATION ALGORITHM
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Genomes / Phylogenetics Plagiarism Music Genres Determining File Types
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PROBLEMS WE CAN'T SOLVE
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COMPLEXITY
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P = NP
?
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COMPLEXITY
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MST all vertices sorting searching point-to-point shortest path primality gcd 2-SAT 3-SAT travelling salesman timetabling MST some vertices Super Mario bin packing P NP
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COMPLEXITY
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MST all vertices sorting searching point-to-point shortest path primality gcd 2-SAT 3-SAT travelling salesman timetabling MST some vertices Super Mario bin packing P NP
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UNCOMPUTABLE FUNCTIONS
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The Halting Problem Kolmogorov Complexity Busy Beaver Chaitin’s Constant
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PROBLEM SOLVING
CS+X 2017 AARON STOCKDILL