Module 12 Computation and Configurations Formal Definition Examples.

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Module 12 Computation and Configurations Formal Definition Examples

Definitions Configuration Computation 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

Computation 1 Line 1, x=?,y=?,r=? Line 2, x=10, y=3,r=? 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

Computation 2 Input: 53 10 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 ...

Computations 1 and 2 Line 1, x=?,y=?,r=? Line 2, x=10, y=3,r=? Output is 1 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 ...

Observation int main(int x,y) { 2 int r = x % y; 3 if (r== 0) goto 8; 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)