Transcript Module 12

Module 12
• Computation and Configurations
– Formal Definition
– Examples
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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
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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
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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
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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
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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
...
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Computations 1 and 2
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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
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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
...
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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; }
• 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)
• Line 3, x= 10, y=3, r=1
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