Curing Cancer with Your Cell Phone: Why all Sciences are Becoming Computing Sciences

David Evans http://www.cs.virginia.edu/evans

Computer Science =

Doing Cool Stuff with Computers?

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Toaster Science =

Doing Cool Stuff with Toasters?

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Computer Science

• Mathematics is about declarative (“what is”) knowledge; Computer Science is about imperative (“how to”) knowledge • The Study of Information Processes – How to describe them Language – How to predict their properties Logic – How to implement them quickly, cheaply, and reliably Engineering

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Most Science is About Information Processes Which came first, the chicken or the egg?

How can a (relatively) simple, single cell turn into a chicken?

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Agenda

• Three Big Ideas: – All Computers are Equally Powerful – Programs are Data, Data are Programs – Many Surprisingly Different Problems are Equally Difficult • One Open Question – Is a machine that can always guess correctly able to solve problems a normal machine can’t?

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“Computers” before WWII

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Mechanical Computing

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Modeling Pencil and Paper

...

# C S S A 7 2 3 ...

How long should the tape be?

“Computing is normally done by writing certain symbols on paper. We may suppose this paper is divided into squares like a child’s arithmetic book.” Alan Turing, On computable numbers, with an application to the Entscheidungsproblem, 1936

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Modeling Brains

•Rules for steps •Remember a little “For the present I shall only say that the justification lies in the fact that the human memory is necessarily limited.” Alan Turing

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Turing’s Model

...

# 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 # ...

Start Input: # Write: # Move:  Input: 1 Write: 1 Move:  1 Input: 0 Write: 0 Move:  2 Input: 1 Write: 0 Move:  Input: 0 Write: # Move:  3

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Universal Machine

Universal Machine A Universal Turing Machine can simulate any Turing Machine running on any Input!

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Church-Turing Thesis

• All mechanical computers are equally powerful* *Except for practical limits like memory size, time, energy, etc.

• There exists a Turing machine that can simulate any mechanical computer • Any computer that is powerful enough to simulate a Turing machine, can simulate any mechanical computer

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What This Means

• Your cell phone, watch, iPod, etc. has a processor powerful enough to simulate a Turing machine • A Turing machine can simulate the world’s most powerful supercomputer • Thus, your cell phone can simulate the world’s most powerful supercomputer (it’ll just take a lot longer and will run out of memory)

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Recap

• All Computers are Equally Powerful • Programs are Data, Data are Programs • Many Problems are Equally Difficult – But no one knows how difficult!

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A “Hard” Problem?

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Generalized Pegboard Puzzle

• Input: a configuration of cracker barrel style pegboard (of any size)

n

pegs on a • Output: if there is a sequence of jumps that leaves a single peg, output that sequence of jumps. Otherwise, output false.

Is this a “hard” problem?

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Solving Problems

• A solution to a problem instance: given a pegboard configuration, here’s the sequence of jumps • A solution to a problem: a procedure that (1) always finds the correct answer, and (2) always finishes.

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“Brute Force” Solvers

• Enumerate all possible answers – Every possible sequence of jumps • Try them all until you find one that works – Simulate the jumps • This works for almost all problems!

• Problem: how long does it take?

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1200

Problem Solving Time

1000 800 ~ 2

n

600 ~

n

3 400 200 0 1 2 3 4 5 6 7 8 Problem Input Size 9

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n

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70000

Increasing Problem Size

~ 2

n

60000 50000 40000 30000 20000 10000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ~

n

3

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1200000 Tractable and Intractable Problems 1000000 800000 600000 400000 “intractable” “tractable” 200000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

I do nothing that a man of unlimited funds, superb physical endurance, and maximum scientific knowledge could not do.

– Batman (may be able to solve intractable problems, but computer scientists can only solve tractable ones for large n)

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time since “Big Bang” 2032 today

This makes a huge difference!

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n

1E+30 1E+28 1E+26 1E+24 1E+22 1E+20 1E+18 1E+16 1E+14 1E+12 1E+10 1E+08 100000 0 10000 100 1 ~

n

3 2 4 8 16 32 64 128 log-log scale

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Back to the Pegboard...

• A brute force solution is easy...but on the pink line • Is there a tractable solution?

1E+30 1E+28 1E+26 1E+24 1E+22 1E+20 1E+18 1E+16 1E+14 1E+12 1E+10 1E+08 100000 0 10000 100 1 2 4 8 16 32 64 128

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Deciding a Problem Is Hard

• “I tried really hard and still couldn’t solve it.” – Maybe the speaker isn’t smart enough – Maybe a few days more effort will find it • “Lots of really smart people tried really hard and no one could solve it.” • “It seems sort of like this other problem that we think is hard...”

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Reduction

Input Trans former Output Trans former Pegboard Solver jumps Hard Problem Solver

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Reading the Genome

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Whitehead Institute, MIT

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Gene Reading Machines

• One read: about 700 base pairs • But…don’t know where they are on the chromosome Read 3 TACCCGTGATCCA Read 1 Actual Genome Read 2 TCCAGAATAA ACCAGAATACC ACCAGAATACCCGTGATCCAGAATAA

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Genome Assembly

Read 1 Read 2 Read 3 ACCAGAATACC TCCAGAATAA TACCCGTGATCCA Input: Genome fragments (but without knowing where they are from) Ouput: The full genome

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Genome Assembly

Read 1 Read 2 Read 3 ACCAGAATACC TCCAGAATAA TACCCGTGATCCA Input: Genome fragments (but without knowing where they are from) Ouput: The smallest genome sequence such that all the fragments are substrings.

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Genome Assembly Solver

ACCAGAATACC TCCAGAATAA TACCCGTGATCCA (~30M reads, ~900 bp) Input Trans former

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Output Trans former Pegboard Solver jumps Genome Assembly Solver

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What This Means

• We already know the shortest common superstring (genome assembly) problem is “hard” • The pegboard problem must also be hard, since we could use a solver for it to solve the genome assembly problem – Requires: we can build fast transformers that don’t increase the problem size exponentially

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...

Non-Deterministic Machines

# 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 # ...

Start Input: # Write: # Move:  1 Input: 1 Write: 1 Move:  Input: 0 Write: 0 Move:  Input: Move: # Write: 0  4 2

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Input: 1 Write: 0 Move:  3

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Non-Deterministic Machine

• Everytime there is a choice, it can guess the correct choice without looking ahead • If we had such a machine, solving Pegboard (or Genome Assembly, etc.) problem would be easy: – It can guess the solution one step (alignment) at a time

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Big Open Question

Is a non deterministic machine able to solve problems that are intractable on a deterministic machine?

1E+30 1E+28 1E+26 1E+24 1E+22 1E+20 1E+18 1E+16 1E+14 1E+12 1E+10 1E+08 100000 0 10000 100 1 2 4 8 16 32 64 128 Seems obvious that the magic guess correctly ability should be useful...but no one knows for sure!

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Recap

• “P vs NP” problem (one of the millennium prize problems) • Solving the pegboard puzzle is equivalent to solving genome assembly • With a non-deterministic machine, we could solve both • With a mechanical computer, we don’t know if a tractable solution exists (but can’t prove it doesn’t): We don’t know if checking a solution is really easier than finding it

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Summary

• Computer Science is the study of information processes: all about problem solving • Many seemingly paradoxical results: – All Computers are Equally Powerful!

– Many Surprisingly Different Problems are Equivalent!

• And seemingly obvious open problems: – Is checking a solution is really easier than finding it?

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Computer Science at UVa

• New Interdisciplinary Major in Computer Science for A&S students (approved last year) • Take CS150 this Spring – Every scientist needs to understand computing, not just as a tool but as a

way of thinking

• Lots of opportunities to get involved in research groups

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My Research Group

• Computer Security: computing in the presence of adversaries • Recent student projects: – Proof that the Pegboard puzzle is hard (Mike Peck and Chris Frost) – Disk-level virus detection (Adrienne Felt) – Web Application Security (Sam Guarnieri) – N-Variant Systems: run variants of a program simultaneously (Sean Talts)

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Questions

http://www.cs.virginia.edu/evans [email protected]

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