1 Module 12 Computation and Configurations –Formal Definition –Important Terms –Examples

2 Computations and Configurations

3 Computations * What is a computation? Is the computation just the output produced by running P on x? –No, we define a computation to be a trace of the entire execution

4 Exercise * 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; } Execute the above program on input

5 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

6 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

7 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: 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...

8 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

9 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? Uncertain Both previous inputs, 10 3 as well as eventually reached above configuration