Chapter 1 Welcome Aboard

Transcription

1 Chapter 1 Welcome Aboard

2 Abstraction Interface Source:

3 evels of Abstraction (Biological System) Source: 1-3

4 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. evels of Abstraction (Computer) Problems Algorithms anguage Instruction Set Architecture Hardware/Software Interface Microarchitecture Circuits Devices 1-4

5 Universal Computing Device All computers, given enough time and memory, are capable of computing exactly the same things. = = Embedded Processor Supercomputer Source: Then what is the simplest possible computing device? 1-5

6 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Turing Machine Mathematical model of a device that can perform any computation Alan Turing (1937) Every computation can be performed by some Turing machine. (Turing s thesis) ( 그럼이세상에계산하지못하는것도있나? Yes Halting Problem We ll discuss it later) For more info about Turing machines, see For more about Alan Turing, see 1-6

7 Tape... A Turing Machine... Control Unit ead-write head Source: Prof. Costas Busch s ecture Slides 1-7

8 The Tape... No boundaries -- infinite length... ead-write head The head moves eft or ight Source: Prof. Costas Busch s ecture Slides

9 ead-write head The head at each transition (time step): 1. eads a symbol 2. Writes a symbol 3. Moves eft or ight Source: Prof. Costas Busch s ecture Slides

10 Example:... Time 0 a a c b Time 1 a b k c eads 2. Writes a k 3. Moves eft Source: Prof. Costas Busch s ecture Slides

11 Computation Example The function f ( x, y) x y is computable x, y are integers Turing Machine: Input string: x0 y unary Output string: xy0 unary Source: Prof. Costas Busch s ecture Slides

12 x y Start q 0 initial state The 0 is the delimiter that separates the two numbers Source: Prof. Costas Busch s ecture Slides

13 x y Start q 0 initial state x y Finish q f final state Source: Prof. Costas Busch s ecture Slides

14 Execution Example: x 11 y 11 (=2) (=2) q 0 x Time 0 y Final esult x y Source: Prof. Costas Busch s ecture Slides

15 Turing machine for function f ( x, y) x y Control Unit q 0 0 1,, q q ,, Source: Prof. Costas Busch s ecture Slides

16 Time q 0 0 1, q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

17 Time q 0 0 1, q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

18 Time q 0 0 1, q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

19 Time q 1 0 1, q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

20 Time q 1 0 1, q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

21 Time q 1 0 1, q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

22 Time q 1 0 1, q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

23 Time q 2 0 1, q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

24 Time , q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

25 Time , q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

26 Time , q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

27 Time , q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

28 Time , q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

29 Time , q0 1 q, q2 1 0,, Source: Prof. Costas Busch s ecture Slides

30 Time , q0 1 q, q2 1 0, HAT & accept Source: Prof. Costas Busch s ecture Slides

31 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Universal Turing Machine A machine that can implement all Turing machines -- this is also a Turing machine! inputs: data, plus a description of computation (other TMs) T add, T mul a,b,c U c(a+b) Universal Turing Machine U is programmable so is a computer! Program is part of the input data a computer can emulate a Universal Turing Machine and vice versa A computer is a universal computing device. 1-31

32 Halting Problem Halting Problem The problem of determining, from a description of an arbitrary computer program (i.e., Turing machine) and an input, whether he program will finish running (i.e., halts) or continue to run forever Halting problem is undecidable (not Turing machine solvable) (Proof by an application of Cantor s diagonal argument) 오토마타교과목에서더깊게다루어짐. 1-32

33 꼭기억해야할것 (evels of) Abstraction Turing Equivalence Undecidable Problem (not Turing machine computable) 1-33