Open Access
Table 3
Loop invariant of the edit distance algorithm
| Step | Outer Loop Invariant Construction |
|---|---|
| INV 1 | i≥1∧ i≤length med∧ j≤length (med!(i 1))∧ j≥1 |
| INV 2 | ((∀k. k < i  ( ∀ j. j<length (med!(k-1))  med!k!j =min_ed_dist0 k j A B ))∧(∀k. k<length med  med!k!0=0) |
| INV 3 | length med≥1∧(∀k .k<length med  length (med!k) = length (med!(k-1)) ∧ length (med!k)≥1 |
| INV4 | INV{INV 1 ∧ INV 2 ∧ INV 3} |
| Step | Inner Loop Invariant Construction |
| INV 1 | i≥1∧ i<length med∧ j≤length (med!(i-1))∧ j≥1 |
| INV 2 | (∀k. k < i  ( ∀ j. j<length (med!(k 1))  med!k!j =min_ed_dist0 k j A B ))∧ ( ∀ k. k < j  med!i!k =min_ed_dist0 i k A B )∧(∀k. k<length med  med!k!0=0) |
| INV 3 | length med≥1 ∧(∀k .k<length med  length (med!k) = length (med!(k-1)) ∧ length (med!k)≥1 |
| INV4 | INV{INV 1 ∧ INV 2 ∧ INV 3} |
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