1. Module 12
Computation and Configurations
Formal Definition
Examples

2. 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

3. 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

4. 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
...

5. 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
...

6. 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 eventually reached the same configuration (Line 3, x=10, y=3, r=1)