Coursepack2 - Module 12 Computation and Configurations...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Module 12 Computation and Configurations Formal Definition Examples
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Definitions Configuration Functional Definition Given the original program and the current configuration of a computation, someone should be able to complete the computation Contents of a configuration for a C++ program current instruction to be executed current value of all variables Computation Complete sequence of configurations
Background image of page 2
3 Computation 1 1 int main(int x,y) { 2 int r = x % y; 3 if (r== 0) goto 8; 4 x = y; 5 y = r; 6 r = x % y; 7 goto 3; 8 return y; } Input: 10 3 Line 1, x=?,y=?,r=? Line 2, x=10, y=3,r=? Line 3, x=10, y=3, r=1 Line 4, x=10, y=3, r=1 Line 5, x= 3, y=3, r=1 Line 6, x=3, y=1, r=1 Line 7, x=3, y=1, r=0 Line 3, x=3, y=1, r=0 Line 8, x=3, y=1, r=0 Output is 1
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Computation 2 int main(int x,y) { 2 int r = x % y; 3 if (r== 0) goto 8; 4 x = y; 5 y = r; 6 r = x % y; 7 goto 3; 8 return y; } Input: 53 10 Line 1, x=?,y=?,r=? Line 2, x=53, y=10, r=? Line 3, x= 53, y=10, r=3 Line 4, x=53, y=10, r=3 Line 5, x=10, y=10, r=3 Line 6, x=10, y=3, r=3 Line 7, x=10, y=3, r=1 Line 3, x=10, y=3, r=1 ...
Background image of page 4
5 Computations 1 and 2 Line 1, x=?,y=?,r=? Line 2, x=53, y=10, r=? Line 3, x= 53, y=10, r=3 Line 4, x=53, y=10, r=3 Line 5, x=10, y=10, r=3 Line 6, x=10, y=3, r=3 Line 7, x=10, y=3, r=1 Line 3, x=10, y=3, r=1 ... Line 1, x=?,y=?,r=? Line 2, x=10, y=3,r=? Line 3, x=10, y=3, r=1 Line 4, x=10, y=3, r=1 Line 5, x= 3, y=3, r=1 Line 6, x=3, y=1, r=1 Line 7, x=3, y=1, r=0 Line 3, x=3, y=1, r=0 Line 8, x=3, y=1, r=0 Output is 1
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 Observation int main(int x,y) { 2 int r = x % y; 3 if (r== 0) goto 8; 4 x = y; 5 y = r; 6 r = x % y; 7 goto 3; 8 return y; } Line 3, x= 10, y=3, r=1 Program and current configuration Together, these two pieces of information are enough to complete the computation Are they enough to determine what the original input was? No! Both previous inputs, 10 3 as well as 53 10 eventually reached the same configuration (Line 3, x=10, y=3, r=1)
Background image of page 6
7 Module 13 Studying the internal structure of REC, the set of solvable problems Complexity theory overview Automata theory preview Motivating Problem string searching
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
8 Studying REC Complexity Theory Automata Theory
Background image of page 8
9 Current picture of all languages Α ll Languages RE-REC Α ll languages - RE Half Solvable Not even half solvable Which language class should be studied further? REC Solvable
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
10 Complexity Theory In complexity theory, we differentiate problems by how hard a problem is to solve Remember, all problems in REC are solvable Which problem is harder and why? Max: Input: list of n numbers Task: return largest of the n numbers Element Input: list of n numbers Task: return any of the n numbers REC RE - REC All languages - RE
Background image of page 10
11 Resource Usage * How do we formally measure the hardness of a problem?
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/25/2008 for the course CSE 460 taught by Professor Torng during the Fall '07 term at Michigan State University.

Page1 / 245

Coursepack2 - Module 12 Computation and Configurations...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online