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
Language
– How to describe them
– How to predict their properties
Logic
– How to implement them
Engineering
quickly, cheaply, and reliably
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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
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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
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Universal Machine
Input
Description
Result tape
of a of
Turing
running
Machine
M on M
Input
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 n pegs on a
cracker barrel style pegboard (of any
size)
• 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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Problem Solving Time
1200
1000
Time
800
~ 2n
600
~ n3
400
200
~
n
0
1
2
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Problem Input Size
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10
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Increasing Problem Size
70000
~ 2n
60000
50000
40000
30000
20000
10000
~ n3
0
1
2
3
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Tractable and Intractable Problems
1200000
1000000
800000
“intractable”
600000
400000
“tractable”
200000
0
1
2
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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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This makes a huge difference!
time
since
“Big
Bang”
~ 2n
1E+30
1E+28
1E+26
1E+24
1E+22
1E+20
1E+18
1E+16
1E+14
1E+12
2032
today
1E+10
1E+08
100000
0
10000
~ n3
100
1
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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
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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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Output
Input
Reduction
Input
Transformer
Pegboard
Solver
Output
Transformer
jumps
Hard Problem Solver
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Reading the Genome
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 2
Read 1
Actual
Genome
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TCCAGAATAA
ACCAGAATACC
ACCAGAATACCCGTGATCCAGAATAA
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Genome Assembly
Read 1
ACCAGAATACC
Read 2
TCCAGAATAA
Read 3
TACCCGTGATCCA
Input: Genome fragments (but
without knowing where they are
from)
Ouput: The full genome
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Genome Assembly
Read 1
ACCAGAATACC
Read 2
TCCAGAATAA
Read 3
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
ACCAGAATACCCGTGATCCAGAATAA
(~30M reads,
~900 bp)
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Input
Transformer
Pegboard
Solver
Output
Transformer
jumps
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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
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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 nondeterministic
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
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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
evans@cs.virginia.edu
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