Recursive structure of MOS scales: Difference between revisions
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Case 1.1: | Case 1.1: | ||
w₂: <L ... sXL ... sXL ... sXL ... sXL ...L] (complete chunks followed by one or more L's) | |||
w₃: <L ... sXL ... sXL ... sXL ... s> (complete chunks only) | |||
This implies that the last chunk is bigger than the first one, a contradiction because w₂ begins in λ. | This implies that the last chunk is bigger than the first one, a contradiction because w₂ begins in λ. | ||
Case 1.2: | Case 1.2: | ||
w₁: s[something with k s's] | |||
w₂: <L ... sXL ... sXL ... sXL ... s> (complete chunks only) | |||
w₃: <L ... sXL ... sXL ... sXL ... s> (complete chunks only) | |||
So W₂(L<sup>r+1</sup>s, L<sup>r</sup>s) has k+1 chunks, a contradiction. | So W₂(L<sup>r+1</sup>s, L<sup>r</sup>s) has k+1 chunks, a contradiction. | ||
| Line 439: | Line 439: | ||
Case 1.3: | Case 1.3: | ||
w₂: <L ... sXL ... sXL ... sXL ... sXL ...L] (complete chunks followed by one or more L's) | |||
w₃: [... sXL ... sXL ... sXL ... sXL ... s> (one or more L's followed by an s, followed by complete chunks) | |||
or | or | ||
Case 1.4: | Case 1.4: | ||
w₂: <L ... sXL ... sXL ... sXL ... s> (complete chunks only) | |||
w₃: [... sXL ... sXL ... sXL ... sXL ... s> (one or more L's followed by an s, followed by complete chunks) | |||
(both 1.3 and 1.4 imply w₃ has one more s than w₂). | (both 1.3 and 1.4 imply w₃ has one more s than w₂). | ||