Recursive structure of MOS scales: Difference between revisions

Revision as of 19:14, 15 April 2021 view source Jollybard (talk \| contribs) 13 edits Put the proofs in their own section at the bottom Tag: Visual edit ← Older edit		Revision as of 22:44, 15 April 2021 view source Jollybard (talk \| contribs) 13 edits →Uniqueness and existence of the generator Tag: Visual edit Newer edit →
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	Every MOS can be reduced to nL 1s (or 1L ns). Each step of the reduction decreases either the number of L's or the number of s's (or both), so one of them must reach 1 at some point. ''(note that reducing further gets us to 1L 0s, which has a period, but no generator per se)''		Every MOS can be reduced to nL 1s (or 1L ns). Each step of the reduction decreases either the number of L's or the number of s's (or both), so one of them must reach 1 at some point. ''(note that reducing further gets us to 1L 0s, which has a period, but no generator per se)''

	It is clear that the MOS nL 1s has a unique generator, ~~either L~~ or s. However, the previous proof showed that reduction reflects generators, and so by induction all MOS scales have a single generator.		It is clear that the MOS nL 1s has a unique generator, s (or its inversion). However, the previous proof showed that reduction reflects generators, and so by induction all MOS scales have a single generator.