Lecture1.ppt

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R. Rao, CSE 599 Week 1: Introduction and Overview, Theoretical Foundations (Part I)
Welcome to CSE 599
 Instructor: Rajesh Rao (rao@cs.washington.edu)
 TA: Aaron Shon (aaron@cs.washington.edu)
 Class web page
 http://www.cs.washington.edu/education/courses/599/CurrentQtr/
 Add yourself to the mailing list see the web page
 Today’s lecture:
 Course Introduction
 What is Computation?
 History of Computing
 Theoretical Foundations: Part I

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Course goals
 To examine the future of computing
 Moore's law will certainly end. What are the alternatives?
 Biologically-inspired and quantum computing
 To broaden your perspectives on the fundamental aspects of
computation
 To give you sufficient exposure to
 understand the premises of alternative computing paradigms
 allow you to pursue these topics further
 What we will not accomplish
 Mastery of any specific field

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What we will cover
 Background topics
 Theoretical foundations of computer science
 Silicon technology and digital computer organization
 Information theory and thermodynamics
 DNA computing
 Using DNA-binding properties to solve computationally hard
problems
 Neural computing
 Computation in animal brains and in artificial neural networks
 Quantum computing
 Using quantum superposition for massively parallel computation

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Sequence of Lecture Topics
1. Theoretical Foundations of Computer Science (Jan 4 & 11)
2. Silicon Technology and Digital Computing (Jan 18,
including a guest lecture by Chris Diorio, UW)
3. DNA Computing (Jan 25, including a guest lecture by Anne
Condon, UBC)
4. Neural Computing (Feb 1 & 8)
5. Information Theory and Thermodynamics (Feb 15)
6. Quantum Computing (Feb 22, including a guest lecture by
Dan Simon, Microsoft Research)

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Grading, homework, and other logistics
 Grading: Homeworks 50%, Mini-Project 50%
 Homework assignments will be handed out on the day of the
lecture related to the homework (see Course web page)
 Homeworks are due at the beginning of class on the
specified due date (see Course web page)
 Pick a mini-project related to a course topic (project ideas
will appear on Course web…or come up with your own!)
 Project presentations: beginning of March
 Project reports due: finals week (Mar 12-15)

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OK, enough about the course.
Let’s get started…
What is computation?
What does it mean to “compute” something?
What is a computer?

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What is a computer?
 Consider the following:
 A coffee filter
 A wheat threshing machine
 A handful of spaghetti
 Can these be viewed as computers??

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Yes, if you can find a useful mapping…
 For example, consider the handful of spaghetti
 Suppose you want to sort 100 numbers
 Take 100 sticks of spaghetti and cut them to the length of
your numbers
 Hold the spaghetti sticks and align their bottom ends on a
table
 Pick out the tallest stick, then the next tallest, and so on…
 You have just sorted your 100 numbers using a spaghetti
“computer”!

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So, what is a computer?
 A working definition:
 A computer is a physical system whose:
 physical states can be seen as representing elements of another
system of interest
 transitions between states can be seen as operations on these
elements
 Three basic steps:
1. Input data is coded into a form appropriate for physical system
2. Physical system shifts into a new state
3. Output state of system is decoded to extract results of computation
 Consider these 3 steps for our spaghetti computer example.
Also holds for silicon, DNA, neural, and quantum computers.

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If computers can have such varied substrates, how
did we end up with silicon-based digital computers
on our desks (rather than, say, organic, spaghetti-
manipulating analog computers)?
Answer: Because of a convergence of theoretical
and practical ideas in the history of computing…

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A Brief History of Computing
 The early years:
 Mapping numbers to objects (e.g. stones)
 Adding and subtracting by manipulation
 Stonehenge (~ 2800 BC) – a prehistoric computer of solar eclipses?
 The first personal “calculator” –
the abacus (a mnemonic aid
based on place-value notation)

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Early pioneers in software and hardware…
 Muhammad ibn Musa Al’Khorizmi
 Proposed the concept of an “algorithm”
as a written process that achieves a
certain goal when executed
 Published first book on “software”
(12th century)
 Blaise Pascal
 Built a mechanical adding machine
in 1642
 Numbers mapped to dials and gears
 Based on differential transmission via
gears of different sizes

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The middle ages (1800-1900)…
 First software-based controller (1801):
 J.-M. Jacquard’s Automatic Loom
 Control program written on punched
cards
 Babbage’s ideas for steam-powered computers
 Difference Engine (1822) for computing mathematical tables
 Analytical Engine (1833) for general computation (introduced conditionals)
 Both were never constructed

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Punched cards and digital computing…
 Used by Hollerith to input data to his “Tabulating machine”
for tabulating and counting census information (1890)
 Perforated strips of discarded movie film used by Zuse to
control the first programmable digital computers (Z1-Z3)

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The digital computer revolution
 ~1850: George Boole invents Boolean algebra
 Maps logical propositions to symbols
 Allows us to manipulate logic statements using mathematics
 1936: Alan Turing develops the formalism of Turing Machines
 1945: John von Neumann proposes the stored computer program concept
 1946: ENIAC: 18,000 tubes, several hundred multiplications per minute
 1947: Shockley, Brattain, and Bardeen invent the transistor
 1956: Harris introduces the first logic gate
 1972: Intel introduces the 4004 microprocessor
 Present: <0.2 m feature sizes; processors with >20-million transistors

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What is computable?
 We have examined how developments in theory and technology paved
the way for the digital computers we use today
 A key concept that allowed general purpose computing: the stored
program idea
 Theoretical roots: Turing machines, Machines simulating other machines,
Universal Turing Machines
 Church-Turing Thesis: The Turing machine is equivalent in
computational ability to any general mathematical device for
computation, including digital computers.
 Important Result: There exist functions that are not computable by any
computational device

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5 minute break….
(Next: Theoretical foundations of computing)

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Introduction
 We asked what computation was - now we’ll try to answer
the question “what is computable?”
 These results about computability are fundamental.
 They apply regardless of the machine
 But they don’t answer all of our questions
 One of the major contributions of theoretical CS: negative
results

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Abstract Models of Computation
 We want to answer fundamental questions:
 What can we do in a reasonable amount of time?
 What can we do in a reasonable amount of space?
 What can we do at all?
 AMAZING result-- some things are not computable!

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A First Model for Computation: Automata
 Chalkboard Example…(automata for Parity, from Feynman
text, chapter 3)

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Languages
 A language is some set of strings
 The language of a FA is the set of strings the FA recognizes
 In the parity example, we can write
 L = 0* (1 0* 1)* 0*

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In-Class Exercise
 Design a Finite Automata that accepts strings where the
number of 1’s AND the number of 0’s is even…

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Limitations of DFA’s
 Cannot recognize some languages e.g. balanced parens, 0n1n
 Only a finite number of states, so it can’t count.
 We can actually characterize what languages DFA’s
recognize exactly
 Called regular languages

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The Chomsky Hierarchy of Languages
Finite Automata
Regular Languages e.g.
parity
Pushdown Automata
Context-Free Languages
e.g. 0n1n
Linear Bounded
Automata
Context Sensitive
Languages e.g. anbncn
Turing Machines
Recursively Enumerable
Languages

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DFA’s vs. Computers
 Technically, computers are DFA’s
 BUT- we think they can answer questions like 0n1n
 They actually can’t-- what if n was 10100?
 We think of computers as storing numbers, instead of
moving to a state which represents storing that number, but
the general notion is the same

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Turing Machine
 Equivalent to a finite automaton that has an unbounded tape
 Has a head which can move left or right, as well as write
symbols on the tape
 The TM is aware of what the head is looking at
 Can defined as a “program” or list of quintuples:
 (current state, current symbol on tape) to
(next state, new symbol to write, direction of head movement), or
 (q, s, q’, s’, d)
 There exists an initial state q0 and a set of halting states

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An Example of a Turing Machine
 A Turing Machine for checking if parentheses are balanced
(from Feynman text, chapter 3)
 E.g. Tape contains …E()E…, or …E(()(E…, or
…E((()()))E…

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Exercise on Turing Machines…
 Design a Turing machine that multiplies two unary numbers
 Example: Tape contains …111X11…
Answer should be: …111111…
 For a complete solution, see the handout (chapter 28 of The
Turing Omnibus by Dewdney)

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Solution Sketch
 A TM that multiplies unary numbers
 Example: Tape contains …111X11…
Answer is: …111111…
 Pseudocode: On input string w:
1. Write a * to the left of the input to separate the output from input
2. For each 1 occurring after the X:
1. For each 1 occurring before the X:
Write a 1 in the leftmost blank cell of the tape beyond the *
End for
End for
3. Erase the * and all symbols to the right of it
4. Halt

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Alternate Models of TMs
 Multitape TMs
 equivalent to ordinary TMs
 TMs with Rectangular Grids
 TM that can jump to arbitrary locations on the tape
 Nondeterministic TMs
 equivalent to TM in terms of computability
 Will play an important role in the next class

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The stage is set to tackle the big questions…
 What functions are computable?
 We can now ask: Are there functions that a Turing machine cannot
compute?
 What functions are tractable?
 For what type of problems do fast and efficient algorithms exist?
 By efficient, we mean time- and space-efficient
 This will then allow us to look at:
Problems that are hard to solve on conventional computers but can be
solved more efficiently using alternative computing methods such as
DNA, neural, or Quantum Computing

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Next week: Theoretical Foundations (Part II)
 Turing machines that simulate other Turing machines
 Universal Turing machines
 Halting problem and Undecidability
 Computational Complexity: Time and Space Efficiency
 P, NP, and NP-complete problems
Read the handout given today and Feynman chapters 1-3…
Have a great weekend!

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