Complexity of Term Rewriting
Complexity of Term Rewriting
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Proof. Only if. There is a desirable variable assignment. Note that \D\ = J + 1. Suppose the assignment is Xj — > a, (l < i < n) where a; denotes either a[ or a[. Construct 9 D' as follows: By rule rj, ii„, - is rewritten to f{a\g{bbb)... G{bhh)E). Then a\ passes from the left to the right and simulates the values of the m clauses. By rule r^, we get f{a2g{bbb)... G(bbb)E). Repeat the passing process. At last we get f{S'TT... TE) which will be rewritten to A^. The total number of steps is 1 + n{m + 1) + 1 = n{Tn + 1) + 2 = J. Hence, \D'\ < \D\. If. Note that in order to rewrite to A'^ in < |I?|(= J + I) steps, rule re cannot be used; otherwise, at least J + 1 steps are needed. First the initial term tin, must go through rule rj and then goes through r2 and r^. By rj and r^, an assignment is selected, while by r2, the values are passed to all clauses. To rewrite to TV in < J + 1 steps, the rewriting process must go through r^. The left side is f{S'TT... TE), that means all clauses are satisfied.
What to read after Complexity of Term Rewriting?
You can find similar books in the "Read Also" column, or choose other free books by Ke Li to read online
To quickly assess the difficulty of the text, read a short excerpt:
Proof. Only if. There is a desirable variable assignment. Note that \D\ = J + 1. Suppose the assignment is Xj — > a, (l < i < n) where a; denotes either a[ or a[. Construct 9 D' as follows: By rule rj, ii„, - is rewritten to f{a\g{bbb)... G{bhh)E). Then a\ passes from the left to the right and simulates the values of the m clauses. By rule r^, we get f{a2g{bbb)... G(bbb)E). Repeat the passing process. At last we get f{S'TT... TE) which will be rewritten to A^. The total number of steps is 1 + n{m + 1) + 1 = n{Tn + 1) + 2 = J. Hence, \D'\ < \D\. If. Note that in order to rewrite to A'^ in < |I?|(= J + I) steps, rule re cannot be used; otherwise, at least J + 1 steps are needed. First the initial term tin, must go through rule rj and then goes through r2 and r^. By rj and r^, an assignment is selected, while by r2, the values are passed to all clauses. To rewrite to TV in < J + 1 steps, the rewriting process must go through r^. The left side is f{S'TT... TE), that means all clauses are satisfied.
What to read after Complexity of Term Rewriting?
You can find similar books in the "Read Also" column, or choose other free books by Ke Li to read online
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